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Chapter 10: Problem 17

The amount of heat required will be minimum when a body is heated through (A) \(1 \mathrm{~K}\) (B) \(1^{\circ} \mathrm{C}\) (C) \(1^{\circ} \mathrm{F}\) (D) It will be the same in all the three cases

Short Answer

Expert verified
The minimum amount of heat will be required when the body is heated through \(1^{\circ} \mathrm{F}\). This corresponds to Option (C).

Step by step solution

01

Identifying the Smallest Temperature Change

Start by identifying which of the options corresponds to the smallest change in temperature. Though Kelvin (K) and degree Celsius (掳C) are equivalent in terms of temperature change (i.e., 1K = 1掳C), they are larger than a change of 1 degree Fahrenheit (掳F). A change of 1掳F is approximately equal to a change of 0.56掳C or 0.56K.
02

Linking Temperature Change to Amount of Heat

Since the amount of heat required to change the temperature of a body is directly proportional to the change in temperature, it follows that the smallest change in temperature will require the least amount of heat. As established in Step 1, a change of 1掳F represents the smallest change in temperature.
03

Choosing the Correct Option

Based on the calculation from Step 2, it can be concluded that the amount of heat required will be minimum when a body is heated through 1掳F. This corresponds to Option (C).

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Most popular questions from this chapter

1000 drops of a liquid of surface tension \(\sigma\) and radius \(r\) join together to form a big single drop. The energy released raises the temperature of the drop. If \(\rho\) be the density of the liquid and \(S\) be the specific heat, the rise in temperature of the drop would be \((J=\) Joule's equivalent of heat) (A) \(\frac{\sigma}{J r S \rho}\) (B) \(\frac{10 \sigma}{J r S \rho}\) (C) \(\frac{100 \sigma}{J r S \rho}\) (D) \(\frac{27 \sigma}{10 J_{r} S \rho}\)

An aluminium sphere of \(20 \mathrm{~cm}\) diameter is heated from \(0^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\). Its volume changes by (given that the coefficient of linear expansion for aluminium \(\left.\alpha_{A l}=23 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) (A) \(28.9 \mathrm{cc}\) (B) \(2.89 \mathrm{cc}\) (C) \(9.28 \mathrm{cc}\) (D) \(49.8 \mathrm{cc}\)

The radius of a metal sphere at room temperature \(T\) is \(R\) and the coefficient of linear expansion of the metal is \(\alpha .\) The sphere heated a little by a temperature \(\Delta T\) so that its new temperature is \(T+\Delta T\). The increase in the volume of the sphere is approximately. (A) \(2 \pi R \alpha \Delta T\) (B) \(\pi R^{2} \alpha \Delta T\) (C) \(4 \pi R^{3} \alpha \Delta T / 3\) (D) \(4 \pi R^{3} \alpha \Delta T\)

A cubic vessel (with face horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of \(500 \mathrm{~ms}^{-1}\) in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground (A) Remains the same because \(500 \mathrm{~ms}^{-1}\) is very much smaller than \(v_{\mathrm{rms}}\) of the gas. (B) Remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls. (C) Will increase by a factor equal to \(\left(v_{\mathrm{mns}}^{2}+(500)^{2}\right) / v_{\mathrm{mns}}^{2}\), where \(v_{\mathrm{rms}}\) was the original mean square velocity of the gas. (D) Will be different on the top wall and bottom wall of the vessel.

A wire fixed at the upper end stretches by length \(l\) by applying a force \(F .\) The work done in stretching is [2004] (A) \(F / 2 l\) (B) \(F l\) (C) \(2 F l\) (D) \(F l / 2\)
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