Q4 of 51 Page 62

Calculate the change in internal energy of a gas kept in a rigid container when 100 J of heat is supplied to it.

Given


Heat supplied ΔQ = 100J


From first law of thermodynamics, we know that,


ΔQ=ΔU+ΔW


Where ΔQ=heat supplied to the system


ΔU=change in internal energy


ΔW=work done by the system


We know that,


Work done = force ×displacement



Volume = areadisplacement


Therefore,


Work done=pressure ×volume


Let change in the volume of system = ΔV = V2-V1


Pressure =P


Thus, work done by the gas


ΔW=PΔV


Since the gas is kept in a rigid container, therefore ΔV=0 in this case.


So, ΔW=0


Thus, first law will become


ΔQ=ΔU = 100J


∴ change in internal energy will be 100J.


More from this chapter

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2

Figure shows a paddle wheel coupled to a mass of 12 kg through fixed frictionless pulleys. The paddle is immersed in a liquid of heat capacity 4200 JK–1 kept in an adiabatic container. Consider a time interval in which the 12 kg block falls slowly through 70 cm.

(a) How much heat is given to the liquid?


(b) How much work is done on the liquid?


(c) Calculate the rise in the temperature of the liquid neglecting the heat capacity of the container and the paddle.



 3

A 100 kg block is started with a speed of 2.0 m
s–1 on a long, rough belt kept fixed in a horizontal position. The coefficient of kinetic friction between the block and the belt is 0.20.

(a) Calculate the change in the internal energy of the block-belt system as the block comes to a stop on the belt.


(b) Consider the situation com a frame of reference moving at 2.0 m s–1 along the initial velocity of the block. As seen from this frame, the block is gently put on a moving belt and in due time the block starts moving with the belt at 2.0 ms–1. Calculate the increase in the kinetic energy of the block as it stops slipping past the belt.


(c) Find the work done in this frame by the external force holding the belt.


 5

The pressure of gas changes linearly with volume from 10 kPa, 200 cc to 50 kPa, 50 cc.

(a) Calculate the work done by the gas.


(b) If no heat is supplied or extracted from the gas, what is the change in the internal energy of the gas?


 6

An ideal gas is taken from an initial state i to a final state f in such a way that the ratio of the pressure to the absolute temperature remains constant. What will be the work done by gas?