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Chapter 19: Q50P (page 580)

We give $70 鈥� J$ as heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase?

Short Answer

Expert verified

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Step by step solution

01

Given data

Heat energy given to a diatomic gas is $Q = 70 J$

02

Understanding the concept

The expression for the amount of energy transferred to the gas is given by,

$Q = n C_{V} 螖 T$

Here Q is the amount of energy transferred to gas,n is the number of moles, $C_{v}$ is the specific heat capacity at constant volume and $螖 T$ is the temperature difference.

03

Calculate by how much the internal energy of the gas increases

$螖 E_{i n t} = {nC}_{V} 螖 T$

But, for diatomic gas $, C_{V} = \frac{5}{2} R$

Hence,

$螖 E_{i n t} = \frac{5}{2} n R 螖 T$ 鈥︹€� (i)

Also, $Q = n C_{P} 螖 T$

But, for diatomic gas $C_{P} = \frac{7}{2} R$

Hence,

$\begin{matrix} Q = \frac{7}{2} n R 螖 T \\ n R 螖 T = \frac{2}{7} Q \end{matrix}$

Substitute $\frac{2}{7} Q$ for $n R 螖 T$ into the equation (i)

$螖 E_{i n t} = \frac{5}{2} (\frac{2}{7} Q)$

Substitute $70 鈥� J$ for Q into the above equation,

$鈬� 螖 E_{i n t} = 50 鈥塉$

Therefore, the increase in the internal energy is $50 J .$

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Most popular questions from this chapter

An ideal gas is taken through a complete cycle in three steps: adiabatic expansion with work equal to $125 鈥� J$ , isothermal contraction at $325 K$ , and increase in pressure at constant volume.

(a) Draw a p-V diagram for the three steps

. (b) How much energy is transferred as heat in step3, and

(c) is it transferred to or from the gas?

A sample of ideal gas expands from an initial pressure and volume of 32atmand $1.0 L$ to a final volume of $4.0 鈥� L$ . The initial temperature is $300 鈥� K$ . If the gas is monatomic and the expansion isothermal, what are the (a) final pressure $P_{f}$ , (b) final temperature $T_{f}$ , and (c) work W done by the gas? If the gas is monatomic and the expansion adiabatic, what are (d) $P_{f}$ , (e) $T_{f}$ , and (f) W? If the gas is diatomic and the expansion adiabatic, what are (g) $P_{f}$ , (h) $T_{f}$ , and (i) W?

Question: An air bubble of volume 20 cm³is at the bottom of a lake 40 mdeep, where the temperature is 4. 0 ⁰C. The bubble rises to the surface, which is at a temperature of. Take the temperature of 20 ⁰C the bubble鈥檚 air to be the same as that of the surrounding water. Just as the bubble reaches the surface, what is its volume?

An ideal gas initially at pressure $p_{0}$ undergoes free expansion until its volume is $3.00$ times its initial volume. What then is the ratio of its pressure to $p_{0}$ ?
The gas is next slowly and adiabatically compressed back to its original volume. The pressure after compression is ${(3.00)}^{1 / 3} p_{0}$ . Is the gas monoatomic, diatomic or polyatomic?
What is the ratio of the average kinetic energy per molecule in this final state to that in initial state?

Figure shows a cycle undergone by 1.00molof an ideal monoatomic gas. The temperatures are T₁=300K, T₂=600K and T₃=455K.For $1 鈫� 2$ , what are- (a)Heat Q (b)The change in internal energy $螖 E_{i n t}$ (c) The work done W? For $3 鈫� 1$ , (d) What is Q? (e) What is Q? (f) What is W? For $3 鈫� 1$ , (g)What is Q?(h) What is $螖 E_{i n t}$ ? (i) What is W? For the full cycle, (j) What is Q? (k)What is $螖 E_{i n t}$ ? (l) What is W? The initial pressure at point 1 is 1.00atm.What are the (m) volume and (n) pressure at point 2? What are the (o) volume and (p) pressure at point 3?

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