Question

A monoatomic ideal gas initially at 17°C is is suddenly compressed to one-eighth of its original volume. The temperature after compression is:
a)16°C b)17°C c)887°C d)none of these.

Answer 1

Answer on Question#38157, Physics, Other

Question:

A monoatomic ideal gas initially at $17{}^{\circ}\mathrm{C}$ is suddenly compressed to one-eighth of its original volume. The temperature after compression is:

a) $16{}^{\circ} \mathrm{C}$

b) $17{}^{\circ} \mathrm{C}$

c) $887{}^{\circ} \mathrm{C}$

d) none of these.

Answer:

"Sudden compression" means that the gas is squeezed so fast that heat does not have a chance to enter or leave the gas. Therefore it is adiabatic process:

$$TV^{\gamma - 1} = const$$

For a monatomic ideal gas $\gamma = \frac{5}{3}$

$$T_0 V_0^{\frac{2}{3}} = T_1 \left(\frac{V_0}{8}\right)^{2/3}$$ $$T_1 = 8^{\frac{2}{3}} T_0 = 4 T_0 = 4 * (17 + 273) K = 1160\,K$$

Answer: d) none of these