Heat is supplied to a sample of a monatomic ideal gas at 40 °C.It is observed that the gas expands until its volume and pressure are doubled.What is the final temperature of the gas?

Question

Quizplus · Accepted Answer

The final temperature of the gas can be found using the ideal gas law, $PV = nRT$, where $P$ is pressure, $V$ is volume, $T$ is temperature in Kelvin, $n$ is the amount of substance, and $R$ is the ideal gas constant. Since both the volume and pressure are doubled, the final state can be represented as $2P \times 2V = nR(T_f)$, where $T_f$ is the final temperature. The initial state is $PV = nRT_i$, where $T_i$ is the initial temperature in Kelvin. Given that the initial temperature is 40 °C, which is 313 K, and considering the relationship between the initial and final states, we can deduce that the final temperature must be 4 times the initial temperature (since both pressure and volume are doubled, the right side of the equation is 4 times larger). Therefore, $T_f = 4 \times 313 K = 1252 K$, which is approximately 980 °C.

Heat Is Supplied to a Sample of a Monatomic Ideal