Thermodynamics Terms

The coefficient of performance ( ) of a refrigerator is defined as the ratio of the heat extracted from the cold reservoir to the work input required to pump the heat to the hot reservoir. The formula for is: where: is the temperature inside the freezer (cold reservoir) in Kelvin, is the temperature of the surroundings (hot reservoir) in Kelvin. Step 1: Convert the temperatures to Kelvin.
The temperature inside the freezer is , which is equivalent to: The coefficient of performance ( ) is given as 5, so we know: Step 2: Solve for .
Substitute the known values into the formula for : Rearrange the equation to solve for : Substitute and : Simplify: Now, add 253 to both sides: Step 3: Convert back to Celsius.
Now, convert back to Celsius: Rounding this off, we get: Thus, the temperature of the surroundings is .

For an isothermal expansion of an ideal gas, the work done by the gas is given by: Where: - is the work done by the gas, - is the number of moles of the gas, - is the universal gas constant, - is the temperature, - is the final volume, - is the initial volume. First, we calculate the number of moles of the gas using the ideal gas equation: Substitute the given values: Now, calculate the work done: Thus, the work done by the gas is .