Fill in the blanks:
$1.$ The change of internal energy in a cyclic process is ......
$2.$ The internal energy of a gas is increased by ......
$3.$ An ideal gas at temperature $T_1$ is compressed to $1/32$ of its original volume,then its temperature $T_2$ will be ...... $(\gamma = 1.4)$.
$4.$ The triple point of water is at ...... pressure and ...... temperature.

(N/A) $1.$ In a cyclic process,the system returns to its initial state. Since internal energy is a state function,the change in internal energy is $0$.
$2.$ The internal energy of a gas increases when work is done on the gas in an adiabatic process (where $Q = 0$,$\Delta U = -W$).
$3.$ For an adiabatic process,$T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$. Given $V_2 = V_1 / 32$ and $\gamma = 1.4$,we have $T_2 = T_1 (V_1 / V_2)^{\gamma-1} = T_1 (32)^{1.4-1} = T_1 (32)^{0.4} = T_1 (2^5)^{2/5} = T_1 \times 2^2 = 4 T_1$.
$4.$ The triple point of water occurs at a pressure of $4.58 \text{ mm Hg}$ and a temperature of $273.16 \text{ K}$.