Question

A quantity of ideal gas requires 800 kJ to raise the temperature of the gas by 10.0 K when the gas is maintained at constant volume. The same quantity of gas requires 900 kJ to raise the temperature of the gas by 10.0 K when the gas is maintained at constant pressure. What is the adiabatic gas constant of this gas

Answer 1

Answer:

$\gamma=1.125$

Explanation:

From the question we are told that:

Initial Heat $Q_1=800kJ$

initial Temperature $T_1=10.0K$

Final Heat $Q_2=800kJ$

Final Temperature $T_2=10.0K$

Generally the equation for Adiabatic constant is mathematically given by

$\gamma=\frac{Cp}{Cv}$

Since

Equation for Heat $dQ=nCdT$

Where

$n_1=n_2\\\\T_1=T_2$

Therefore

$Q_1=Cv\\\\Cv=800$

And

$Cp=900$

Therefore

$\gamma=\frac{900}{800}\\\\\gamma=\frac{9}{8}$

$\gamma=1.125$