Question

A sample of ideal gas has internal energy ‘U’ and is then compressed to one half of its original volume. While the temperature remains the same. The ratio of final internal energy U’ to initial internal energy U is

(1) 1/4

(2) 1/2

(3) 1

(4) 2

Answer 1

(3) 1

For an ideal gas 

PV = nRT 

where dU = nC_VdT

as temperature remains constant in the process, dT = 0

Hence there is no change in internal energy dU = U’– U = 0

Hence U'/U = 1