Question

In an engine, an almost ideal gas is compressed adiabatically (see Note below) to half its volume. In doing so, 2630 Joules of work is done on the gas. (a) How much heat flows into or out of the gas? (b) What is the change in internal energy of the gas? (c) Does its temperature rise or fall? Note: An adiabatic process is one that occurs without transfer of heat or matter between a thermodynamic system and its surroundings. In an adiabatic process, energy is transferred only as work.

Answer 1

Solution:

Before solving this question we should have some basic ideas in thermodynamics.

• In an adiabatic process, there will be no heat flow in or out of the system. ie dQ=0
• According to the first law of thermodynamics, dQ= dU+dW

Sign convention: Work done on the system is taken as negative and work done by the system is taken as positive( Opposite way also can be taken. Sign reverses in that case).

a) Since the process is adiabatic, heat flow is zero. ie dQ= zero

b) From first law of thermodynamics, dQ= dU+dW

0= dU+dW

dU= -dW Here work is done on the system. Therefore dW= -2630 J

Therefore internal energy dU= 2630 J Here there is an increase in internal energy.

c) Internal energy U can be written as U= 1/2* f k T f is number of degrees of freedom, k is Boltzman constant and T is temperature. Since the internal energy is increasing, temperature also will be increasing.

or internal energy U= ³/₂RT (internal energy of ideal gas is directly proportional to temperature.)