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german
1 month ago
12

Three moles of an ideal gas with a molar heat capacity at constant volume of 4.9 cal/(mol∙K) and a molar heat capacity at consta

nt pressure of 6.9 cal/(mol∙K) starts at 300 K and is heated at constant pressure to 320 K, then cooled at constant volume to its original temperature. How much heat flows into the gas during this two-step process?
Physics
1 answer:
ValentinkaMS [3.4K]1 month ago
7 0

Answer:

The amount of heat that enters the gas throughout this two-step process totals 120 cal.

Explanation:

Given that,

Moles present = 3

Heat capacity at volume held constant = 4.9 cal/mol.K

Heat capacity at pressure held constant = 6.9 cal/mol.K

Starting temperature = 300 K

Ending temperature = 320 K

We are tasked with determining the heat absorbed by the gas at constant pressure

Employing the heat formula

\Delta H_{1}=nC_{p}\times\Delta T

Substituting the values into the equation

\Delta H_{1}=3\times6.9\times(320-300)

\Delta H_{1}=414\ cal

Next, we calculate the heat absorbed by the gas at constant volume

Using the corresponding heat formula

\Delta H_{1}=nC_{v}\times\Delta T

Insert the values into the formula

\Delta H_{1}=3\times4.9\times(300-320)

\Delta H_{1}=-294\ cal

Now, it's necessary to evaluate the total heat flow into the gas during both steps

Using the total heat formula

\Delta H_{T}=\Delta H_{1}+\Delta H_{2}

\Delta H_{T}=414-294

\Delta H_{T}=120\ cal

Thus, the heat that transfers into the gas throughout this two-step process amounts to 120 cal.

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