2. A student living in a 3-m × 4-m × 4-m dormitory room turns on her 100-W fan before she leaves the room on a summer day, hoping that the room will be cooler when she comes back in the evening. Assuming all the doors and windows are tightly closed and disregarding any heat trans-fer through the walls and the windows, determine the temperature in the room when she comes back 8 h later. Use specific heat values at room temperature and assume the room to be at 100 kPa and 20°C in the morning when she leaves.

The room temperature will be

Explanation:

We know from First law of thermodynamics that the amount of heat flow (Q) through a system is given by

where, 'm' is the mass of the system, is the specific heat and is the temperature difference. Also we know, = 0.718 KJ .

According to the problem, the heat flow can also be written as

So,

Again, if 'm' be the mass of the gas and 'R' be the Universal gas constant = then from Ideal gas equation we can write,

So,

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