A body of water loses ebq03ij m)cwur,)p5 (b twld9inergy at a constant rate. Assume that the specific heat capacity of ice is hali5tdp 9l()bqb ,im j0crwwu 3)f the specific heat capacity of liquid water.
Which graph shows a possible variation of temperature with time

  A chemical reaction occurs inside a solmj3cwo e. sj2 r*:pg,kid of mass $m$ and specific heat capacity $c$. The initial temperature of the solid is $50\,K$.
What is the minimum energy that the reaction must release to increase the temperature of the solid to $100^{\circ}C$?

  An immersion heater of constant power output is used to supply thermal en5 arf53g/ dinbergy to a cup of water at 373 K. The heater is turned on at time t=0. Which graph shows a possible variation of temperature T of the water, with time a b3di5frng/5t?

  Two solid substances of equal mass are heated with the same power input. The gravij( hq5orl52 k 2c,e88 x8oif2oq lfqph below shows how the temlo8 q,5hl 2jr2(koqiqvif 5x8e2fc 8operatures of the substances vary with time during heating.

Which of the following statements are correct?
I. Substance A has a lower specific heat capacity than Substance B when they are in the same physical state.
II. The specific heat capacity of each substance is lower in the solid state than the liquid state.
III. Substance A has a lower specific latent heat of fusion than Substance B.

  A sealed container contains a mixture of hydrogen and nitrogen grtd5 5:baaaeq l- 1kgf9 qr8.vas.
The ratio ${mass\,of\,a\,hydrogen\,molecule}{mass\,of\,a\,nitrogen\,molecule}$=$\frac{1}{7}$The ratio $\frac{average\,kinetic\,energy\,of\,hydrogen}{average\,kinetic\,energy\,of\,nitrogen}$is

  In an experiment, a liquid-filled beaker is positioned on an electrf iwmwbtmwj ,/ bz89-/onic balance. An immersion heater with a power rating of P is introduced into the water. Once the water begins to /w zjbi8m,-ww f9bm t/boil, a researcher monitored the change in mass m of the liquid over time t once the boiling commenced.

The theoretically predicted relationship between time $t$ and $m$ is $L_v$​=$frac{Pt}{C−m}$​
$C$ is the initial mass of the liquid when $t=0\,s$ and $L_v$​ is the latent heat of vaporisation of water.
1.Give the units of $L_v$​ in fundamental SI units.
2.In a particular experiment, the researcher uses a heater of power 65.0±0.1 W and measures m=0.120±0.001kg, C=0.125±0.001 kg, and t=600±1 s.
(1)Calculate the percentage error in the measured value of $L_v$​. $The\,percentage\,error\,of\,L_v$​
=    %
(2)For this experiment, calculate the value of $L_v$​ and its absolute uncertainty. $L_v$​ =    $\times10^6\,Jkg^{-1}$
(3)The accepted value of $L_v​$ is $2.3\times10^6\,Jkg^{−1}$. Explain why the experimental value does not match the accepted value.
3.The researcher plots a graph to show how m varies with $t$.
(1)Outline why P must be kept constant during the experiment.
(2)Assuming the relationship $L_v$​=$\frac{Pt}{C−m}$​ is correct, sketch the expected mass-time relationship on the axes below. (There is no need to put numbers to the axes).


(3)Outline how to obtain the value of $L_v$​ from the graph you have drawn in c(ii).

  Two ideal gases $A$ and $B$ of molar masses $m_A​>m_B$​ are initially at absolute temperatures $T_A​

  A material with a mass of m is he gnjj 687lsdypdcwj0 s499xp;ated. The graph shows the variation of the temperature of the material with the en6x8sg nc0 j9ys4pl ;ddj7pwj9ergy supplied.

Which one of the following gives the specific heat capacity of the material?

  A spherical object of c x-9gaqb.i2)4wim 0hm q n20/qiomtjsurface area $A$ and absolute temperature $T$ can be regarded as a black body. The power of the radiation emitted from the object is $P$. What would be the power of the radiation emitted by an object with an absolute temperature of $2T$and a surface area of $\frac{A}{2}$​?

  Water in a beaker is heatequ23 7z1nh nrs((kd (/0vjov/sfq e rfd on a hot plate at a rate P. The graph shows the change in temperature of the wat7vq/rqu0f (z 3ovkr sd(h(nf n/j 12eser over time.

Which graph correctly shows the new change in temperature of the water when the rate of thermal energy transfer is increased?
The original graph is shown by the dotted line.

  1,Define specific heat capacv xm9( shoxb: :f vebqms.e0:,ity.
2,A sample of a substance initially in the solid state of mass of 200 g is heated by a heater of constant power. The variation of the temperature T with time t is shown on the graph below.

(1)The specific heat capacity of the sample in the liquid state is $1400\,J\,kg^{−1}K^{−1}$. Determine the power of the heater. P =    W
(2)Determine the specific latent heat of vaporization of the sample. L =   $J\,kg^{−1}$
(3)Explain, by considering the molecular model, why the time needed to boil the sample is more than the time needed for melting the same sample.
(4)It is realized that some of the sample in the liquid state evaporates during the heating process. State two differences between evaporation and boiling.

  An object has a surfa/y lr fs/j+jhadk4r22:b vym7ce area of $2.0\,m^2$ and emissivity $e=0.5$. The object emits electromagnetic radiation of peak wavelength $2.90\times10^{−5}\,m$. What is the best estimate for the energy radiated by the object in one second?

  1.A “Newton's cradle” contains a row of five touching metal balls, e kqiwkyl2( .5tach of mass 1.0 g and specific heat capacq2t 5k.lwyi(k ity 400 $J\,kg^{-1}\,K^{−1}$, suspended from light strings of length 30 cm.
With its string kept taut, Ball 1 is released from rest at an angle of $60^{\circ}C$ to the vertical, causing it to collide with the other four balls. During every resulting collision, the moving ball comes to rest and most of its kinetic energy is transferred to the ball on the opposite end of the row. The remaining three balls remain stationary. It can be assumed that the size of each ball is negligible. $ΔT_{max}​$ =    mK

Assuming all energy from the ball is converted to thermal energy in the balls, determine the temperature increase of the five balls after the system has come to rest.
2.Explain why changing the mass of each ball, without altering its material, does not affect the final temperature.
3.(1)Balls 2-5 are replaced with an ice block of mass 9.0 g. Ball 1 is thrown horizontally so that it embeds itself in the ice at a velocity of 10.0 $m\,s^{−1}$. The ball/ice system slides frictionlessly along the surface after the collision. Determine speed of the system as it slides. $v_f$ =    $m\,s^{-1}$
(2)Show that the amount of energy converted to thermal energy in the collision is 45 mJ. $E_{heat}$ ​=    mJ
4.Estimate the percentage of the ice that melts, assuming that no energy is lost from the system. The system is at an initial temperature of $0^{\circ}C$.
Specific latent heat of fusion of ice = 333 $kJ\,kg^{−1}$ Percentage melted is therefore =    %

  Water of mass m at an s;twd 1u*+k5h/kmqbt initial temperature of $20^{\circ}C$ oC is provided with thermal energy at a rate P. Its temperature rises to $30^{\circ}C$ in time t.
The rate of energy transfer is doubled and the mass of the water is halved. What is the final temperature, in time t, if the initial temperature is again $20^{\circ}C$?

  A hot sphere of tempg.3zz;8 3 f gml.mmrouerature T and surface area $A_1$​ radiates towards a metal plate of area $A_2$​ that is a very large distance D away. Which of the following expressions gives the rate at which radiant energy is received by the plate?

  Which of the graphs below best describes the change in average kim+vgj,d/arw1:h lqw4,af:ymlzi2ajsm i +*/netic energy of the molecules of a beaker of water r fmy1 4a vdq:hz+ma+is/gm,l/j*l:iw, jwa2as it is heated at a constant rate until it completely boils away?

  100 ml of water at $20^{\circ}C$ is poured in an aluminum container and heated at a constant rate until all of the water is boiled. After time $t_1$​ water starts to boil, and at time $t_2$ all of the water has boiled away.
Which of the following statements are correct?
I. If a glass container with the same mass is used instead of aluminum, $t_1$​ increases. ($c_glass$<$c_aluminum$​)
II. If the container with water is thermally isolated,$t_2$ decreases.
III. If more water is added to the container, $t_1$  increases.

  1.In an experiment, a beaker containing i0su /4qpk 11b 5/fnve4oyfvpkf6)yt liquid of mass m is heated with a heater of power P. Then tyi/nk y610o41s4efvf pkv/ p)qb5uf the variation of temperature T of the liquid with time t is recorded.

The data from the experiment is shown on the graph below.

(1)On the graph, draw the line of best fit for the data.
(2)Explain why it can not be concluded that the relationship between temperature and time is directly proportional.
2.Theory suggests that
$frac{T-T_0}{t}$=K
where$T_0$​ is the temperature when t=0 s.
(1)Using the data given, calculate the percentage uncertainty of $(T−T_0​$) at time 25s. $T_0$ =    %
(2)Use the graph to determine constant k.
(3)Theory also suggests that another expression for k is given by
$k=frac{P}{mc}$​, where c is another constant.
Determine the units of constant c, expressing your answer in fundamental SI units.

  A 100g chocolate bar is placed onto a (we6 fz7sn ax9hot plate. The chocolate is initially at its melting temperatnae7fw (xz s69ure of $30^{\circ}C$.
Heat is transferred from the plate to the chocolate at a constant rate $P_{in​}$ of 12W, causing it to melt at a constant rate of $6\,g\,min^{−1}$. After all the chocolate has melted, the liquid chocolate continues to heat to a temperature of $353\,K$.
Specific heat capacity of melted chocolate = $1.0\,kJkg^{−1}K^{−1}$
Specific latent heat of fusion of chocolate = $50\,Jg^{−1}$

1.State how the kinetic and potential energy of the chocolate change as it melts.
2.(1)Determine the amount of energy required to heat the liquid chocolate from the melting temperature to 353K. ΔE =    kJ
(2)Show that approximately 58% of the supplied energy is lost to the surroundings while the chocolate is melting. $As\,a\,percentage\,of\,the total energy, this\,gives$ =    %
3.The graph shows how the temperature of the chocolate changes with time.

Draw on the same graph a new line to show how temperature would change for a larger mass of chocolate with the same starting conditions.

  1.An electric heater with a power rating of 2.8 kW hm7rvr pqgw;, zlva*(p1ezo99 eats liquid that flows through i7 9m( lv*,1q9rezpwp;v roga zt. The temperature of the liquid increases from $18^{\circ}C$ to $38^{\circ}C$while passing through the heater. The flow rate of the liquid σ is $0.035\,kgs^{−1}$. Calculate the specific heat capacity of the liquid. c =    $J\,kg^{-1}\,K^{-1}$
2.Suggest whether your answer for (a) is above or below the actual value of the specific heat capacity. Justify your answer.

  1.An object X of surface arpcb) s7lj/5r.y 8eh.v99rqv qegx 3iu ea $24.3\,cm^2$ emits 300W of radiation when its temperature is 1215K.
(1)State what is meant by emissivity.
(2)Show that this object is a blackbody radiator. e ≈   
2.Calculate the peak wavelength of the emitted radiation. $λ_{max}$ =    $\times10^{-6}\,m$
3.The object X is left to cool down until it reaches 800K. On the axes given, sketch the variation of intensity with wavelength of the radiation of object X at both the original 1215K and the cooler temperature of 800K. Label the graphs.

  Black body X at kelvin temperatu, c ;c oxnabq zhi4m/awhy jo.52,.z4wre T has surface area A and total radiation power P. If blaccwa,jym4n ,ao. zcw/z5b.hqx o i ;h42k body Y has temperature 2T and total radiation power of 2P, what is the surface area of Y?

  A pendulum consists of a mass M with a speci )hcc 5/-w5tmbbnh 1wsgb0.gffic heat capacity S suspended from a point by a light string of length L. The pendulum is placed in an insulated container filled with ac-f5h. bs ht 0gmw g)5c/bwnb1 mass 2M of liquid with a specific heat capacity 2S. The pendulum is released from rest with the string horizontal. Assume that acceleration due to gravity is g and that both have the same starting temperature.

If all of the energy from the pendulum is converted to thermal energy, what is the temperature change of the liquid?

  An ice cube of mass m at its melting temperature is placed in a mass M of water yk-dgxl++ dxz0z+x;nat an initial temperat+d+0kxlxzy;x gz - nd+ure of $20^{\circ}C$. Assume that the specific heat capacity of liquid water is $4\,kJ\,kg\,K^{−1}$ and it has a specific latent heat of fusion of $320\,Jg^p{−1}$.

Assuming that the system is thermally isolated , what is the minimum value of M required for the ice to completely melt?

  1.Define the specific latentm ew,6in1xdo ( heat of fusion.
2.An ice cube of temperature $-20^{\circ}C$ and mass 45g is placed in a bottle which is half filled with water of temperature $40^{\circ}C$and mass 1.2kg. Energy transfer only happens between the water and the ice.
The following data is available:
Specific latent heat of fusion of ice =$3.3\times10^5\,Jkg^{−1}$
Specific heat capacity of ice =$2.2\times10^3\,Jkg^{−1}K^{−1}$
Specific heat capacity of water = $4.2\times10^3$ $J$$kg^{−1}K^{−1}$
(1)Determine the final temperature T of the water. T =    $^{\circ}C$
(2)On the graph below, sketch how only the mass of water in the bottle varies with the temperature.
(no need to add values on the axes)

  The graph shows how the temperature of a solid wax block vawxf 5/1wm8 y3wp.nif wries with time. The solid waxpi5wn1.8 mf /w3wf yxw has a specific heat capacity of $2\,kJ\,kg^{−1}K^{−1}$ and it absorbs heat at a rate of 20W.



What is the specific latent heat of fusion of wax?

  A thermally isolated system consists of a coin of weight7m +tp bt kdq0 ac9((c,gdng)w2gp.yk mg and specific heat capacity c suspended in a vacuum at a vertical dist qnyagc pk. d0k2c(d9m p7b+wgt, (gt)ance H above a solid block. The block has mass 4m, specific heat capacity 2c and latent heat of fusion L. The melting temperature of the block is an amount ΔT greater than the initial temperature of the block and the coin. The coin is dropped on to the block.


What is the minimum value of H required for the block to melt due to the collision?

  1.Distinguish between an ideal gas and a non-ideal gas with dse* u-dn,deo33 nm(wue2xn/ mf nx,; reference to the internal ene nu xsedxnn3,m /eod3 wfm, u;2-*(denrgy of the molecules.
2.An ideal gas of mass 20g is heated in a sealed container. The temperature of the gas is increased from $127^{\circ}C$ to $327^{\circ}C$. The specific heat capacity of the gas at constant volume is $2.5\times10^4\,Jkg^{−1}K^{−1}$.
(1)Calculate the increase in total kinetic energy of the molecules of the ideal gas. The increase in total kinetic energy of the ideal gas is =    $\times10^5\,J$
(2)The average speeds of the molecules at $127^{\circ}C$ to $327^{\circ}C$ are $v_i$​ and $v_f$​ respectively. Calculate $\frac{v_i}{v_f}$​. $\frac{v_i}{v_f}$ =   

  A temperature-time graph for t zqc 9 s7:xz:xevn2gw;j:lk e+he heating of 100 g of a substance is shown, from its state as a solid to its state as a gas. The material is being heated in a well-insulated container at a constant heating rate of 50 W. It is assumed tqs+:zxj7nl :xvkg 2 zec:w9;ehat mass remains constant and no heat is lost to the surroundings.

What is the specific heat capacity of the material in the liquid state?

  A substance, initially solid of masjk:a 5)aied/ 0f-hvu js 2.00 kg is heated by a 4.0 kW electric heater causing it to melt. During heating, the substance alsui k5: vd)aj0ah/ jf-eo exchanges heat with its surroundings. The substance starts melting immediately and has fully turned to liquid after 400 s. Given that the specific latent heat of fusion of the solid is $900\,kJkg^{−1}$, what is the average rate of heat transfer between the substance and the surroundings in one second?

  A liquid of mass M, temperature 4T specific heat capacity S is held in an insuwi ih;h1j1o5vlated container of negligible mass. A second liquid of mass 2M, temperature T aoh 15i 1wij;hvnd specific heat capacity 3S is added to the container.
What is the equilibrium temperature of the mixture?

  A thin metal plate of mass m is held at an nwlqcr*zk8g1g 05 apj,** )extc cjs:absolute temperature T, in an enclosure of temperature *a8rwgs: ,q0c*zkcljt xn*e)g1p cj5$T_s$​

  A hollow, insulated ring is packed ww;c66 tdc(xsqz 4g ec6ith a mass M of ice pellets at an initial tempe4dw6q;zt ecgccs( 66xrature of $0^{\circ}C$. A mass 3M of steam is injected into the ring and circulates around it at an initial temperature of $100^{\circ}C$. Assume that the specific latent heat of vaporization is seven times the specific latent heat of fusion L.
L is also equal to the energy required to increase the temperature of a unit mass of liquid water by $80^{\circ}C$.


What are the final states of matter in the ring?

  In order to calculate the spedya6f 7,af7:( wazlb:ea jv n,cific latent heat of fusion of ice, a mass m of ice at a temper,dajlna7: v7ffz : ,e6a(yb awature of $-2^{\circ}C$ was left inside a beaker until it changed into water at $20^{\circ}C$.


If q is the energy needed to make this change for 1 kilogram of ice, the specific heat capacity of ice is $c_i$​, the specific heat capacity of water is $c_w$​, and the specific latent heat of fusion of ice is $L_F$​.
Which expression gives the specific latent heat of fusion of ice $L_F$​?