Question 955: Thermodynamics & KTG

Question

A monatomic gas at a pressure P, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is (Take $$\gamma $$ = 5/3)

Accepted Answer

First, isothermal expansion
$$PV = P'\left( {2V} \right);P' = {P \over 2}$$
Then, adiabatic expansion
$$P'{\left( {2V} \right)^\gamma } = {P_f}{\left( {16V} \right)^\gamma }$$
(For adiabatic process, PV
$$\gamma $$
= constant)
$${P \over 2}\left( {2V} \right) = {P_f}{\left( {16V} \right)^{5/3}}$$
$${P_f} = {P \over 2}{\left( {{{2V} \over {16V}}} \right)^{5/3}} = {P \over 2}{\left( {{1 \over 8}} \right)^{5/3}}$$
$$ = {P \over 2}{\left( {{1 \over {{2^3}}}} \right)^{5/3}} = {P \over 2}\left( {{1 \over {{2^5}}}} \right) = {P \over {64}}$$

Answer

64P

Answer

32P

Answer

P/64

Answer

16P

Thermodynamics & KTG

A monatomic gas at a pressure P, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is (Take $\gamma $ = 5/3)

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