Question

A 1.00kg block of copper at 20degreesC is dropped into a large vessel of liquid nitrogen a -196degressC. How many kilograms of nitrogen boil away by the time the coper reaches -196degressC? The specific heat capacity of coppe is 0.385kJ/gdegressC and the heat of vaporization of nitrogen is 5.57 kJ/mol.

Answer 1

Question #29216, Physics, Other

A 1.00kg block of copper at 20 degrees C is dropped into a large vessel of liquid nitrogen at -196 degrees C. How many kilograms of nitrogen boil away by the time the copper reaches -196 degrees C? The specific heat capacity of copper is 0.385kJ/g degrees C and the heat of vaporization of nitrogen is 5.57 kJ/mol.

Solution.

Find the heat quantity which need take from copper:

$$Q = m(Cu) \cdot C(Cu) \cdot (T_1 - T_2) = 1.00 \cdot 0.385 \cdot (20 - (-196)) = 83.16 \text{ kJ};$$

where $m(Cu)$ – mass of the copper block, kg;

$C(Cu) = 0.385 \text{ kJ/(kg*C)}$ is the specific heat capacity of copper;

This heat is equal to the heat of nitrogen vaporization:

$$Q = \lambda(N_2) \cdot \frac{m(N_2)}{M(N_2)};$$

where $\lambda(N_2) = 5.57 \text{ kJ/mol}$, is the heat of one mole nitrogen vaporization.

$m(N_2)$ – nitrogen mass, kg;

$M(N_2) = 0.028 \text{ kg/mol}$ – nitrogen molar mass;

Find the mass of nitrogen:

$$m(N_2) = \frac{Q \cdot M(N_2)}{\lambda(N_2)} = \frac{83.16 \cdot 0.028}{5.57} = 0.418 \text{ kg};$$

Answer: the mass of nitrogen is 0.418 kg.