Question 826: Thermodynamics & KTG

Question

A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is

Accepted Answer

Given,
$$\begin{aligned}
& p=	ext { Pressure } \
& V=	ext { Volume } \
& m=	ext { mass }
\end{aligned}$$
Now, using Ideal gas law,
$$p V=n R T$$ .... (i)
Here $$n=$$ mass of gas $$=m / M$$
$$R=	ext { Gas constant }$$
$$\because$$ We know that $$p, V$$ and $$m$$ are same for hydrogen and oxygen and from Eq. (i), we have
$$T=\frac{p V}{n R}=\frac{p V M}{m R}$$ ..... (ii)
For oxygen, $$T_{\mathrm{O}_2} \propto M_{\mathrm{O}_2}$$
For hydrogen, $$T_{\mathrm{H}} \propto M_{\mathrm{H}}$$
Now, the ratio of $$T_{\mathrm{O}_2} / T_{\mathrm{H}}$$ is
$$\frac{T_{\mathrm{O}_2}}{T_{\mathrm{H}}}=\frac{M_{\mathrm{O}_2}}{M_{\mathrm{H}}}=\frac{32}{2}=\frac{16}{1}$$
$$	herefore$$ Ratio of $$T_{\mathrm{O}_2}: T_{\mathrm{H}}=16: 1$$

Answer

$$1: 4$$

Answer

$$4: 1$$

Answer

$$1: 16$$

Answer

$$16: 1$$

Thermodynamics & KTG

A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is

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