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Chapter 6: Problem 37

If the internal energy of a thermodynamic system is increased by $300 . \mathrm{J}\( while 75 \)\mathrm{J}$ of expansion work is done, how much heat was transferred and in which direction, to or from the system?

Short Answer

Expert verified
In this thermodynamic process, 375 J of heat was transferred to the system.

Step by step solution

01

Identify the known and unknown variables

We are given: 1. The increase in internal energy, ∆U = 300 J 2. Work done by the system, W = 75 J We need to find the heat transferred, Q, and its direction (to or from the system).
02

Write down the equation for the first law of thermodynamics

The first law of thermodynamics for a closed system can be stated as: ∆U = Q - W where ∆U is the change in internal energy, Q is the heat transferred, and W is the work done by the system.
03

Substitute the known values and find Q

Now we can substitute the given values into the equation: \(300 \text{ J} = Q - 75 \text{ J}\) To solve for Q, add 75 J to both sides of the equation: \(Q = 300 \text{ J} + 75 \text{ J}\)
04

Calculate the heat transferred and determine its direction

Do the arithmetic to find the value of Q: \(Q = 375 \text{ J}\) The sign of Q is positive, which indicates that heat was transferred to the system. If Q was negative, that would mean heat was transferred from the system.
05

Final Answer

In this thermodynamic process, 375 J of heat was transferred to the system.

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Most popular questions from this chapter

In a coffee-cup calorimeter, 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M}\) NaOH and 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M} \mathrm{HCl}\) are mixed. Both solutions were originally at \(24.6^{\circ} \mathrm{C}\) . After the reaction, the final temperature is \(31.3^{\circ} \mathrm{C}\) . Assuming that all the solutions have a density of 1.0 \(\mathrm{g} / \mathrm{cm}^{3}\) and a specific heat capacity of \(4.18 \mathrm{J} / \mathrm{C} \cdot \mathrm{g},\) calculate the enthalpy change for the neutralization of \(\mathrm{HCl}\) by NaOH. Assume that no heat is lost to the surroundings or to the calorimeter.

A sample of an ideal gas at 15.0 atm and 10.0 \(\mathrm{L}\) is allowed to expand against a constant external pressure of 2.00 atm at a constant temperature. Calculate the work in units of kJ for the gas expansion. (Hint: Boyle's law applies.)

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