Five moles of an ideal monatomic gas with an initial...

Five moles of an ideal monatomic gas with an initial temperature of 127$^\circ$C expand and, in the process, absorb 1500 J of heat and do 2100 J of work. What is the final temperature of the gas?

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Key Concepts

First Law of Thermodynamics

This principle states that the change in a system's internal energy is equal to the heat added to the system minus the work done by the system. It provides the energy balance needed to relate the quantities of heat, work, and internal energy change during a thermodynamic process, such as the expansion of a gas.

Internal Energy of an Ideal Monatomic Gas

For an ideal monatomic gas, the internal energy is directly proportional to its temperature and can be calculated using the expression (3/2)nRT, where n is the number of moles and R is the ideal gas constant. This relationship is essential for linking the change in temperature to the energy gained or lost during a process.

Temperature Conversion to Kelvin

Thermodynamic calculations require the use of absolute temperatures. Thus, temperatures given in degrees Celsius must be converted to Kelvin by adding 273.15. This conversion is crucial to ensure that the equations, such as those involving internal energy or the ideal gas law, yield correct results.

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