Match List-I with List-II.
The relations for heat exchange and work done during thermodynamic processes are:
- (A) Isobaric: In an isobaric process (constant pressure), the heat supplied to the system is equal to the work done by the system, i.e., \( \Delta Q = \Delta W \).
- (B) Isochoric: In an isochoric process (constant volume), the change in heat is equal to the change in internal energy, i.e., \( \Delta Q = \Delta U \).
- (C) Adiabatic: In an adiabatic process (no heat exchange), \( \Delta Q = 0 \).
- (D) Isothermal: In an isothermal process (constant temperature), the change in heat is equal to the change in internal energy plus the work done by the system, i.e., \( \Delta Q = \Delta U + P \Delta V \).
Thus, the correct answer is (3).
The remainder when \( 64^{64} \) is divided by 7 is equal to:
x mg of Mg(OH)$_2$ (molar mass = 58) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ____ mg. (Nearest integer) (Given: Mg(OH)$_2$ is assumed to dissociate completely in H$_2$O)