Question 21: Thermodynamics & KTG

Question

A vessel containing 1 mole of $$\mathrm{O}_2$$ gas (molar mass 32) at temperature $$T$$. The pressure of the gas is $$p$$. An identical vessel containing one mole of He gas (molar mass 4) at temperature $$4 T$$ has a pressure of

Accepted Answer

To determine the pressure of the helium (He) gas in the identical vessel, we can use the ideal gas law:
$$PV = nRT$$
Given that both vessels are identical, they have the same volume, $$V$$. Also, each vessel contains one mole of gas, so $$n = 1$$ for both cases. Let's first express the pressure $$p$$ of the oxygen (O
2
) gas in terms of the given conditions:
For the oxygen gas:
$$pV = nRT$$
Substituting the given values:
$$pV = (1 	ext{ mole}) \cdot R \cdot T$$
Therefore,
$$pV = RT$$
Now, consider the helium gas in the other vessel at temperature $$4T$$. According to the ideal gas law:
$$P_{He}V = nRT_{He}$$
Here, $${T_{He} = 4T}$$. Substituting the known values:
$$P_{He}V = (1 	ext{ mole}) \cdot R \cdot (4T)$$
Therefore,
$$P_{He}V = 4RT$$
Since $$pV = RT$$ from our earlier equation for the oxygen gas, we can substitute $$RT$$ with $$pV$$ in the helium pressure equation:
$$P_{He}V = 4(pV)$$
Dividing both sides by $$V$$ to isolate $$P_{He}$$:
$$P_{He} = 4p$$
Therefore, the pressure of the helium gas at temperature $$4T$$ is $$4p$$.
Thus, the correct answer is:
Option C: 4p

Answer

p/8

Answer

p

Answer

4p

Answer

8p

Thermodynamics & KTG

A vessel containing 1 mole of $\mathrm{O}_2 gas (molar mass 32) at temperature T. The pressure of the gas is p. An identical vessel containing one mole of He gas (molar mass 4) at temperature 4 T$ has a pressure of

Choose the correct answer: