## College Physics (4th Edition)

We can rank the cylinders in order of temperature, from highest to lowest: $b = d \gt a = c = e = f$
Let $P_0 = 50~kPa$ Let $V_0 = 2~L$ Let $N_0 = 3\times 10^{23}$ We can find a general expression for the temperature: $P_0~V_0 = N_0~k~T$ $T = \frac{P_0~V_0}{N_0~k}$ We can find an expression for the temperature in each case. (a) $T = \frac{(2P_0)~(2V_0)}{(2N_0)~k} = 2\times \frac{P_0~V_0}{N_0~k}$ (b) $T = \frac{(4P_0)~(2V_0)}{(2N_0)~k} = 4\times \frac{P_0~V_0}{N_0~k}$ (c) $T = \frac{(P_0)~(4V_0)}{(2N_0)~k} = 2\times \frac{P_0~V_0}{N_0~k}$ (d) $T = \frac{(2P_0)~(2V_0)}{(N_0)~k} = 4\times \frac{P_0~V_0}{N_0~k}$ (e) $T = \frac{(2P_0)~(V_0)}{(N_0)~k} = 2\times \frac{P_0~V_0}{N_0~k}$ (f) $T = \frac{(P_0)~(2V_0)}{(N_0)~k} = 2\times \frac{P_0~V_0}{N_0~k}$ We can rank the cylinders in order of temperature, from highest to lowest: $b = d \gt a = c = e = f$