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Chapter 8: Problem 1151

If a quantity of heat \(1163.4 \mathrm{~J}\) is supplied to one mole of nitrogen gas, at room temperature at constant pressure, then the rise in temperature is \(\mathrm{R}=8.31\\{\mathrm{~J} /(\mathrm{m} \cdot 1 . \mathrm{k})\\}\) (A) \(28 \mathrm{~K}\) (B) \(65 \mathrm{~K}\) (C) \(54 \mathrm{~K}\) (D) \(40 \mathrm{~K}\)

Short Answer

Expert verified
The rise in temperature when a quantity of heat (1163.4 J) is supplied to one mole of nitrogen gas at room temperature at constant pressure is approximately 40 K. Therefore, the correct option is (D) \(40\,\mathrm{K}\).

Step by step solution

01

Write down the formula for heat capacity at constant pressure

We will use the formula for heat capacity at constant pressure (Cp) for an ideal gas: \[ q = nC_p∆T \] where q = heat supplied (1163.4 J), n = number of moles (1 mole), Cp = heat capacity at constant pressure, ∆T = rise in temperature.
02

Determine the heat capacity at constant pressure for nitrogen gas

For diatomic molecules like nitrogen gas, the molar heat capacity at constant pressure (Cp) can be calculated by adding the gas constant R to the molar heat capacity at constant volume (Cv), which would result in the equation: \[ C_p = C_v + R \] For a diatomic molecule, the molar heat capacity at constant volume (Cv) is given by the equation: \[ C_v = \dfrac{5}{2} R \] Substitute the value of Cv in Cp formula: \[ C_p = \dfrac{5}{2} R + R \]
03

Calculate Cp using the given value of R

Now, substitute the given value of R in the Cp formula: \[ C_p = \dfrac{5}{2}(8.31) + (8.31) \] \[ C_p = 20.775 + 8.31 = 29.085 \, \mathrm{J/(mol.K)} \]
04

Solve for the rise in temperature (∆T)

Now, we have all the necessary values to find the rise in temperature (∆T). The formula that we will use is: \[ ∆T = \dfrac{q}{nC_p} \] Substitute the given values: \[ ∆T = \dfrac{1163.4 \,\mathrm{J}}{1\,\mathrm{mol} \times 29.085\, \mathrm{J/(mol.K)}} \]
05

Calculate the final answer

Calculate the final value of the rise in temperature: \[ ∆T = \dfrac{1163.4}{29.085} = 39.96 \approx 40\,\mathrm{K} \] The rise in temperature when a quantity of heat (1163.4 J) is supplied to one mole of nitrogen gas at room temperature at constant pressure is approximately 40 K. Therefore, the correct option is (D) \(40\,\mathrm{K}\).

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Most popular questions from this chapter

Carnot engine working between \(300 \mathrm{~K}\) and \(600 \mathrm{~K}\) has work output of \(800 \mathrm{~J}\) per cycle. What is amount of heat energy supplied to the engine from source per cycle (A) \(1600\\{\mathrm{~J} /\) (cycle)\\} (B) \(2000\\{\mathrm{~J} /(\mathrm{cycle})\\}\) (C) \(1000\\{\mathrm{~J} /(\) cycle \()\\}\) (D) \(1800\\{\mathrm{~J} /(\) cycle \()\\}\)

A diatomic gas initially at \(18^{\circ} \mathrm{C}\) is Compressed adiabatically to one eighth of its original volume. The temperature after Compression will be (A) \(10^{\circ} \mathrm{C}\) (B) \(668 \mathrm{~K}\) (C) \(887^{\circ} \mathrm{C}\) (D) \(144^{\circ} \mathrm{C}\)

Instructions :Read the assertion and reason carefully to mask the correct option out of the options given below. (A) If both assertion and reason are true and the reason is the correct explanation of the assertion. (B) If both assertion and reason are true but reason is not be correct explanation of assertion. (C) If assertion is true but reason is false. (D) If the assertion and reason both are false. Assertion : A beakers is completely, filled with water at $4^{\circ} \mathrm{C}$. It will overflow, both when heated or cooled. Reason: These is expansion of water below \(4^{\circ} \mathrm{C}\) (A) \(\mathrm{A}\) (B) B (C) C (D) D

In a container of negligible heat capacity, 200 g ice at $0^{\circ} \mathrm{C}\( and \)100 \mathrm{~g}\( steam at \)100^{\circ} \mathrm{C}$ are added to \(200 \mathrm{~g}\) of water that has temperature \(55^{\circ} \mathrm{C}\). Assume no heat is lost to the surroundings and the pressure in the container is constant \(1 \mathrm{~atm}\). At the final temperature, mass of the total water present in the system is (A) \(493.6 \mathrm{~g}\) (B) \(483.3 \mathrm{~g}\) (C) \(472.6 \mathrm{~g}\) (D) \(500 \mathrm{~g}\)

One mole of a monoatomic gas is heat at a constant pressure of 1 atmosphere from \(0 \mathrm{k}\) to \(100 \mathrm{k}\). If the gas constant $\mathrm{R}=8.32 \mathrm{~J} / \mathrm{mol} \mathrm{k}$ the change in internal energy of the gas is approximate ? (A) \(23 \mathrm{~J}\) (B) \(1.25 \times 10^{3} \mathrm{~J}\) (C) \(8.67 \times 10^{3} \mathrm{~J}\) (D) \(46 \mathrm{~J}\)
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