A hypothetical gas expands adiabatically such that its volume changes from 8 litres to 27 litres. If the ratio of final pressure to initial pressure is 16/81, then the ratio $C_{P}$ / $C_{V}$ will be:
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Question

A hypothetical gas expands adiabatically such that its volume changes from 8 litres to 27 litres. If the ratio of final pressure to initial pressure is 16/81, then the ratio $C_{P}$ / $C_{V}$ will be:

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G1 Physics · Accepted Answer

For an adiabatic process, P(V)^γ = constant. Thus P(f)/P(i) = [V(i)/V(f)]^γ = (8/27)^γ = (2/3)^(3γ). Since 16/81 = (2/3)^4, we get 3γ=4, so γ = 4/3.

A hypothetical gas expands adiabatically such that its volume changes from 8 litres to 27 litres. If the ratio of final pressure to initial pressure is 16/81, then the ratio C P C_{P} C P ​ / C V C_{V} C V ​ will be:

A hypothetical gas expands adiabatically such that its volume changes from 8 litres to 27 litres. If the ratio of final pressure to initial pressure is 16/81, then the ratio C P C_{P} C P / C V C_{V} C V will be: