Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 14, Problem 49P
To determine

The final temperature of the system.

Expert Solution & Answer
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Answer to Problem 49P

The final temperature of the system is T=32°C_.

Explanation of Solution

Write the expression for heat required to melt ice.

Q=miceLf+miceciceΔT (I)

Here, Q is the heat, mice is the mass, cice is the specific heat capacity of ice, ΔT is the temperature, and Lf is the latent heat of fusion.

Write the expression for heat absorbed from water.

|Q|=mwcw|ΔT| (II)

Here, mw is the mass of water, and cw is the specific heat capacity of water

Write the expression for the total heat flow in the system.

Qw+Qice=0mwcwΔTw+miceLf+miceciceΔT1+micecwΔT2=0 (III)

Substitute TTw for ΔTw, (273.15KTice) for ΔT1, and (T273.15K) for ΔT2 in equation (III) and rearrange to obtain an expression for T.

micecice(273.15KTice)+micecw(T273.15K)=mwcw(TTw)+miceLf(mwcw+micecw)T+miceLf+mice(cicecw)(273.15K)=mwcwTw+miceciceTice=0T=mwcwTw+miceciceTicemiceLfmice(cicecw)(273.15K)cw(mw+mice) (IV)

Conclusion:

Substitute, 0.075kg for mice, 333.7kJ/kg for Lf, 2.1kJ/kgK for cice, and 10K ΔT in equation (I).

Q=(0.075kg){333.7kJ/kg+[2.1kJ/kgK](10K)}=27kJ

Substitute, 0.50kg for mw, 4.186kJ/kgK for cw, 50K for ΔT in equation (II).

|Q|=0.50kg×4.186kJ/kgK×50K=105kJ

Since, the 105kJ>27kJ ice will melt completely.

Substitute, 0.50kg for mw, 4.186kJ/kgK for cw, (50.0+273.15)K for Tw, 0.075kg for mice, (10+273.15)K for Tice, 333.7kJ/kg for Lf, 2.1kJ/kgK for cice in equation (IV)

T=(0.50kg)(4.186kJ/kgK)((50.0+273.15)K)+(0.075kg){[2.1kJ/kgK](10+273.15)K333.7kJ/kg}(0.075kg)[2.1kJ/kgK4.186kJ/kgK](273.15K)(4.186kJ/kgK)(0.50kg+0.075kg)=305.2K273.15K=32°C

Therefore, the final temperature of the system is T=32°C_.

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Chapter 14 Solutions

Physics

Ch. 14.5 - Prob. 14.8PPCh. 14.5 - Prob. 14.9PPCh. 14.6 - Prob. 14.6CPCh. 14.6 - Prob. 14.10PPCh. 14.6 - Prob. 14.11PPCh. 14.8 - Prob. 14.12PPCh. 14.8 - Prob. 14.8CPCh. 14.8 - Prob. 14.13PPCh. 14.8 - Prob. 14.14PPCh. 14.8 - Prob. 14.15PPCh. 14 - Prob. 1CQCh. 14 - Prob. 2CQCh. 14 - 3. Why do lakes and rivers freeze first at their...Ch. 14 - Prob. 4CQCh. 14 - Prob. 5CQCh. 14 - Prob. 6CQCh. 14 - Prob. 7CQCh. 14 - Prob. 8CQCh. 14 - 9. What is the purpose of having fins on an...Ch. 14 - Prob. 10CQCh. 14 - Prob. 11CQCh. 14 - 12. Explain the theory behind the pressure cooker....Ch. 14 - Prob. 13CQCh. 14 - Prob. 14CQCh. 14 - Prob. 15CQCh. 14 - Prob. 16CQCh. 14 - Prob. 17CQCh. 14 - Prob. 18CQCh. 14 - Prob. 19CQCh. 14 - Prob. 20CQCh. 14 - Prob. 21CQCh. 14 - Prob. 22CQCh. 14 - Prob. 23CQCh. 14 - Prob. 24CQCh. 14 - Prob. 25CQCh. 14 - Prob. 26CQCh. 14 - 1. The main loss of heat from Earth is by (a)...Ch. 14 - Prob. 2MCQCh. 14 - Prob. 3MCQCh. 14 - Prob. 4MCQCh. 14 - Prob. 5MCQCh. 14 - Prob. 6MCQCh. 14 - Prob. 7MCQCh. 14 - Prob. 8MCQCh. 14 - Prob. 9MCQCh. 14 - Prob. 10MCQCh. 14 - Prob. 11MCQCh. 14 - Prob. 12MCQCh. 14 - Prob. 1PCh. 14 - Prob. 2PCh. 14 - Prob. 3PCh. 14 - Prob. 4PCh. 14 - Prob. 5PCh. 14 - Prob. 6PCh. 14 - Prob. 7PCh. 14 - Prob. 8PCh. 14 - Prob. 9PCh. 14 - Prob. 10PCh. 14 - Prob. 11PCh. 14 - Prob. 12PCh. 14 - Prob. 13PCh. 14 - Prob. 14PCh. 14 - Prob. 15PCh. 14 - Prob. 16PCh. 14 - Prob. 17PCh. 14 - Prob. 18PCh. 14 - Prob. 19PCh. 14 - Prob. 20PCh. 14 - Prob. 21PCh. 14 - Prob. 22PCh. 14 - Prob. 23PCh. 14 - Prob. 24PCh. 14 - Prob. 25PCh. 14 - Prob. 26PCh. 14 - Prob. 27PCh. 14 - Prob. 28PCh. 14 - Prob. 29PCh. 14 - Prob. 30PCh. 14 - Prob. 31PCh. 14 - Prob. 32PCh. 14 - Prob. 33PCh. 14 - Prob. 34PCh. 14 - Prob. 35PCh. 14 - Prob. 36PCh. 14 - Prob. 37PCh. 14 - Prob. 38PCh. 14 - Prob. 39PCh. 14 - Prob. 40PCh. 14 - Prob. 41PCh. 14 - Prob. 42PCh. 14 - Prob. 43PCh. 14 - Prob. 44PCh. 14 - 45. Is it possible to heat the aluminum of Problem...Ch. 14 - Prob. 46PCh. 14 - Prob. 47PCh. 14 - Prob. 48PCh. 14 - Prob. 49PCh. 14 - Prob. 50PCh. 14 - Prob. 51PCh. 14 - Prob. 53PCh. 14 - Prob. 52PCh. 14 - Prob. 54PCh. 14 - Prob. 55PCh. 14 - Prob. 56PCh. 14 - Prob. 57PCh. 14 - Prob. 58PCh. 14 - Prob. 59PCh. 14 - Prob. 60PCh. 14 - Prob. 61PCh. 14 - Prob. 62PCh. 14 - Prob. 63PCh. 14 - Prob. 64PCh. 14 - Prob. 65PCh. 14 - Prob. 66PCh. 14 - 67. One cross-country skier is wearing a down...Ch. 14 - Prob. 68PCh. 14 - Prob. 69PCh. 14 - Prob. 70PCh. 14 - Prob. 71PCh. 14 - Prob. 72PCh. 14 - Prob. 73PCh. 14 - Prob. 74PCh. 14 - Prob. 75PCh. 14 - Prob. 76PCh. 14 - Prob. 77PCh. 14 - Prob. 78PCh. 14 - Prob. 79PCh. 14 - Prob. 80PCh. 14 - Prob. 81PCh. 14 - Prob. 82PCh. 14 - Prob. 83PCh. 14 - Prob. 84PCh. 14 - Prob. 85PCh. 14 - Prob. 86PCh. 14 - Prob. 87PCh. 14 - Prob. 88PCh. 14 - Prob. 89PCh. 14 - Prob. 93PCh. 14 - Prob. 91PCh. 14 - Prob. 92PCh. 14 - Prob. 94PCh. 14 - Prob. 95PCh. 14 - Prob. 96PCh. 14 - Prob. 97PCh. 14 - Prob. 98PCh. 14 - Prob. 99PCh. 14 - Prob. 100PCh. 14 - Prob. 101PCh. 14 - Prob. 102PCh. 14 - Prob. 103PCh. 14 - Prob. 104PCh. 14 - Prob. 105PCh. 14 - Prob. 106PCh. 14 - Prob. 107PCh. 14 - Prob. 108PCh. 14 - Prob. 109PCh. 14 - Prob. 110PCh. 14 - Prob. 112PCh. 14 - Prob. 111PCh. 14 - 116. It requires 17.10 kJ to melt 1.00 × 102 g of...Ch. 14 - Prob. 113PCh. 14 - Prob. 90PCh. 14 - Prob. 115PCh. 14 - Prob. 116PCh. 14 - Prob. 117PCh. 14 - Prob. 118PCh. 14 - Prob. 119PCh. 14 - Prob. 120P
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