A body of water loses energy at a constant rate. Assume that the speclek-/ ku6( mciific heat capacity of ice is hal/(lem ki-cu6 kf the specific heat capacity of liquid water.
Which graph shows a possible variation of temperature with time

  A chemical reaction occurs insideq pmkek:+ i(;xd)p 8yew -ugm( a solid 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)5 :8vbei mmjv output is used to supply thermal energy to a cup of water at 373 K. The heater is turned on at time t=0. Which grmjveb i8: v5m)aph shows a possible variation of temperature T of the water, with time t?

  Two solid substances of er7kt+nvv.c( qaff oqnm d m 73)ojo+0(qual mass are heated with the same power input. The graph below shows how the temperatures of the substances vary wit7+ o)ofja co + m.3r(kd q7vmn0fvqn(th 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 64ri g6,9dygtt 6h 2imb euikl3wf,g4a mixture of hydrogen and nitrogen gas.
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-f-+camfz3q+ jp illed beaker is positioned on an electronic balance. An immersion heater with a power rating of P is introduced into the water. Once the water begins to boil, a resc+z+ fqj-ap3mearcher 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 o e bte.j m d6953pyzjtngl:1:of m is heated. The graph shows the variation of the temperature of the material with the energy s e . 1ldg63pyztb9:5j o:mtnjeupplied.

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

  A spherical object of surface arodl b-s5.82vov.c k-yl /n yp;v (mkdlea $A$ 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 heated on a hot plate at a rate P. The grap 631;2 wrhgy ottz8eddh shows the change in ted8 ze;t owt12hg6ryd 3mperature of the water 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 cm3s*mek;ki79 xp uk 6mapacity.
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 surf:x:oq0j qix8 aace 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” contaqtrt1(:ii t659sj x hcins a row of five touching metal balls, each of mass 1.0 g and specific heat ca9tq5jrithtix 1 6(cs: pacity 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 a7l;skm0jz)q cv nl6, nhd6ab4zd*(qhn 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 temperature T and surface ar su x 5b7vp d2n)8 ff2g6nwfpq4f))8k.ejszv sea $A_1$​ 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 kw q47al(a5ea qinetic energy of the molecwq5a7la(aeq 4ules of a beaker of water as 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 liquid of mass m is doov(4 0 dyztgte:k w7q8/s ;lheated with a heater of power P. Then the variation of temperatut(q dg/ woke7oy0dtl s;84v:zre 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 hot p2mi 6q 9hthwr4late. The chocolate is initially at its meh2 t9ri 46whqmlting temperature 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 e7/pp s3 e9a7to ,qdfna power rating of 2.8 kW heats liquid that flows through it. The temperature of the la9e,/f7n7p3 e psqdto iquid 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 ar7m nsoe- fa:(/p:jywhea $24.3\,cm^2$ 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 kelviv zu6 b+fu79n0l ;yj(nuya)gen temperature T has surface area A and total radiation power P. If black body Y has temperature 2T and total radiation power of 2P, what is njg 9ua n+7fue;b)l vyy u0z(6the surface area of Y?

  A pendulum consists of a mass M with a specififd 7nuwbce6 7v9 z)kv*9+gd phc heat capacity S suspended from a point by a light string of len)* 6d7dkwz9 +nce7gp ubvv h9fgth L. The pendulum is placed in an insulated container filled with a 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 aq* q-y 5ln3,gqc4 cguu mass M of water at an initianc53 uc4qqqg-,ly u* gl temperature 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 latent heat ofdzr d1ycod/u47nh 3kduk0sh f)+0: os 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 varierp3e7xvdtc w r7y/ jolz:b, 7;s with time. The solid wax has a specific heat capacity ;ro7vycw7 /7 zxjberl, :pt3dof $2\,kJ\,kg^{−1}K^{−1}$ and it absorbs heat at a rate of 20W.



What is the specific latent heat of fusion of wax?

  A thermally isolated system,2lus5yaxvc85 wr k2wr*-r 6om8wmw p consists of a coin of weight mg and specific heat capacity c suspended in a vacuum at a vertical distance H above a solid block. The block has sx2kcw*28 ,ou8 r5wplmv wr wymr-5 a6mass 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 idee3j, (ua5tuhj; zxd(g2ioi n*: n 2dvaal gas and a non-ideal gas with reference to the internal energy of the mh2t udn(i,zoa e* ax523d;jjvng i(:uolecules.
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 the heatinghm/ )7ixht)q yen b-v6 of 100 g of a substance is shown, from its state as a solid to its state as a gas. T-7/e)x )b6tivyh hn qmhe material is being heated in a well-insulated container at a constant heating rate of 50 W. It is assumed that 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 ma xe9c q-i2g8frss 2.00 kg is heated by a 4.0 kW electric heater causing it to melt. During heating, the substance also exchanges heat with its surroundings. The substance starts melting immediately and has fully turned to liquier89-gix2cf q d 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, t8fo ypijoag-ua 3 r1m7 ,t7l;femperature 4T specific heat capacity S is held in an insulated container of negligible mass. A second liquid of mass 2M, temperature T and specific heat capacity 3S is added to tuf7 ;joolra ymtai g7,3f8-1phe container.
What is the equilibrium temperature of the mixture?

  A thin metal plate of mass m is held at an absolute tehr4ns +,s0wu lmperature T, in an enclosure of temu+h ,0lsrn4swperature $T_s$​

  A hollow, insulated ring is packed with a masmhu - uhfbb)-o(/as0hs M of ice pellets at an initial temperatuh0fsbo(b-uh-)hu a m/re 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 specific.llu2:7q gtym v98sb y latent heat of fusion of ice, a mass m of ice at 8vlt qm:ybs7 g 2ylu.9a temperature 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 $L_F$​?