Question 953: Thermodynamics & KTG

Question

A diatomic gas undergoes adiabatic change. Its pressure $$p$$ and temperature $$T$$ are related as $$p \propto T^x$$, where $$x$$ is

Accepted Answer

For a diatomic gas undergoing an adiabatic change, the relationship between pressure ($p$) and temperature ($T$) is defined by:
$$\frac{T^\gamma}{p^{\gamma-1}} = 	ext{constant}$$
This equation can be rearranged to:
$$T^\gamma = 	ext{constant} 	imes p^{\gamma - 1}$$
By simplifying further, we find:
$$p \propto T^{\frac{\gamma}{\gamma-1}}$$
Given that $p \propto T^x$, we equate the exponents:
$$x = \frac{\gamma}{\gamma-1}$$
For a diatomic gas, the adiabatic index $\gamma$ is $\frac{7}{5}$. Substituting this value, we calculate:
$$x = \frac{\frac{7}{5}}{\frac{7}{5} - 1}$$
This simplifies to:
$$x = \frac{\frac{7}{5}}{\frac{2}{5}} = \frac{7}{2} = 3.5$$
Therefore, for a diatomic gas undergoing an adiabatic process, the value of $x$ is 3.5.

Answer

3.0

Answer

1.5

Answer

2.5

Answer

3.5

Thermodynamics & KTG

A diatomic gas undergoes adiabatic change. Its pressure $p and temperature T are related as p \propto T^x, where x$ is

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