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

`\gamma=1.125`

Step-by-step 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=(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=(900)/(800)\\\\\gamma=(9)/(8)`

`\gamma=1.125`