Three moles of an ideal monatomic gas are at a temperature of 345 K . Then, 2438 J of heat is ad

step 1 Initial temperature of three moles of monodermic gas is 345 Kelvin so we have TI initial tempera

Three moles of an ideal monatomic gas are at a temperature...

Three moles of an ideal monatomic gas are at a temperature of 345 $\mathrm{K}$ . Then, 2438 $\mathrm{J}$ of heat is added to the gas, and 962 $\mathrm{J}$ of work is done on it. 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 the internal energy of a closed system is equal to the heat added to the system minus the work done by the system. It provides a framework for relating heat and work exchanges to changes in the system’s internal energy in various thermodynamic processes.

Internal Energy of an Ideal Monatomic Gas

For an ideal monatomic gas, the internal energy is solely a function of temperature and can be expressed as U = (3/2) nRT, where n is the number of moles, R is the universal gas constant, and T is the temperature. This relationship is crucial for linking thermal energy changes to temperature variations in ideal gases.

Work and Heat Sign Conventions

In thermodynamics, proper attention must be paid to the sign conventions for work and heat. When work is done on the system, it is considered positive, whereas work done by the system is negative. Similarly, heat added to the system increases internal energy and is taken as positive. Understanding these conventions is important for correctly applying the first law in calculations.

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