2024 RI Prelim H2 Phy Paper 3 Answers

Raffles Institution Year 5-6 Physics Department 1 2024 H2 Physics Preliminary Examination Solution Paper 3 1 (a) The internal energy of an ideal gas is just the sum of the microscopic kinetic energy, due to the random motion of its molecules since the microscopic potential energy of an ideal gas is zero. Its internal energy depends only on its state (pressure, volume, temperature) and amount of gas. (b) (i) 1. U Q W = + Since volume is constant, 0W = . ( ) ( )( ) 21 21 2 5 5 33 22 3 2 3 2.0 10 1.5 10 1.0 102 1500.0 1500 J (shown) QU p V pV V p p − = =− =− =   −  == 2. Since 21 1 21 1 23 3 6.2 10 J2 2 6.2 10 299.52 K3 1.38 10 kE kT T − − − = =   ==   From nRpT V= , since volume is constant, 1 1 pnRp T TVT =  =  ( ) 1 1 5 5 0.5 10 299.52 1.0 10 149.76 150 K pTT p = =  ==

Raffles Institution Year 5-6 Physics Department 2 OR 1 1 3 2 2 3 k k E kT ET k = = Since volume is constant, 12 12 22 21 11 2 3 k pp TT p p ETT p p k = ==  2 21 1 2 1 21 5 23 5 22 33 2 13 2 6.2 10 1.5 10 13 1.38 10 1.0 10 149.76 150 K 150 C kk k p E ETT p k k Ep kp − − − = −  =−     =−      = = =  OR 1 kU NE= where N is the number of gas molecules 1 k UN E= ( ) 21 21 21 33 22 3 2 U U U NkT NkT Nk T T  = − =− =− ( ) ( ) ( )( ) ( )( )( ) 21 1 3 12 21 5 2 23 2 3 2 3 2 3 6.2 10 15004 9 1.0 10 2.0 10 1.38 10 149.76 150 K 150 C k k UTT Nk U U E k EU pV k − −− −= = =  =    = = = 

Raffles Institution Year 5-6 Physics Department 3 (ii) The first law of thermodynamics states that the increase in internal energy U is equal to the sum of the work done on the system W and the heat supplied to the system Q, i.e. U Q W = + . Hence Q U W= − . When a unit mass of the gas , heated under constant volume or under constant pressure, experiences a unit rise in temperature, U will be the same since UT  . When the gas is heated at constant volume, there is no work done. W is zero and VQU= . When the gas is heated at constant pressure, work is done by the gas as it expands. W is negative and pQU . The specific heat capacity of a gas is the heat supplied to a unit mass of the gas to cause a unit rise in its temperature i.e. ( ) Qc mT=  . Since pVQQ the specific heat capacity at constant pressure is higher than that at constant volume.

Raffles Institution Year 5-6 Physics Department 4 2 (a) Since k and m are constant, ax− . This implies that the block’s acceleration is proportional to its displacement from the equilibrium position. The negative sign implies that the direction of its acceleration is always opposite to its displacement, pointing towards the equilibrium position. This satisfies the definition for simple harmonic motion. (b) (i) From the graph, 0.60 sT = , 2 0 2.0 10 mx −= ( ) 00 0 2 1 2 2 2.0 100.60 0.20944 0.209 m s vx xT    − − = = = == (ii)