/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 A \(10 \mathrm{~g}\) body is kep... [FREE SOLUTION] | 91影视

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Chapter 11: Problem 21

A \(10 \mathrm{~g}\) body is kept in an enclosure of \(27^{\circ} \mathrm{C}\). For body's temperature \(127^{\circ} \mathrm{C}\), the specific heat \(0.1 \mathrm{~K} \mathrm{cal} / \mathrm{kg}^{\circ} \mathrm{C}\) and surface area \(10^{-3} \mathrm{~m}^{2}\). The \(\left(\sigma=5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2} \mathrm{k}^{4}\right]\) (A) Rate of cooling is \(0.227 \mathrm{ks}^{-1}\) (B) Rate of cooling will be zero at \(400 \mathrm{~K}\) enclosure (C) Cooling does not take place (D) Cooling will be faster at \(127^{\circ} \mathrm{C}\) enclosure

Short Answer

Expert verified
(A) Rate of cooling is \(0.227 \mathrm{ks}^{-1}\).

Step by step solution

01

Convert temperatures to Kelvin

The temperatures given are in degrees Celsius. The Stefan-Boltzmann law requires temperatures to be in Kelvin. To convert from Celsius to Kelvin, add 273 to the Celsius temperature. Therefore, the body's temperature in Kelvin is \(127^{\circ} \mathrm{C} + 273 = 400K\). Similarly, the enclosure's temperature in Kelvin is \(27^{\circ} \mathrm{C} + 273 = 300K\).
02

Apply the Stefan-Boltzmann Law

To find the rate of cooling, apply the Stefan-Boltzmann law, which is \(P = \sigma \cdot A (T^4 - T0^4)\) where P is power (rate of cooling), \(\sigma\) is the Stefan-Boltzmann constant, A is surface area, \(T\) is the temperature of the body and \(T0\) is the temperature of the environment. Substituting the given values, we find \(P = (5.67 \times 10^{-8}) \cdot (10^{-3}) ((400)^4 - (300)^4).\))
03

Calculate the equation

Solve the equation to find P, which is the rate of cooling. The result should be \(0.227 \mathrm{ks}^{-1}\)

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Most popular questions from this chapter

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