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Chapter 19: Q. 44 (page 545)

The specific heat of most solids is nearly constant over a wide temperature range. Not so for diamond. Between 200 K and 600 K,

the specific heat of diamond is reasonably well described by c = 2.8T - 350 J/kg K, where T is in K. For gemstone diamonds, 1 carat = 200 mg. How much heat energy is needed to raise the temperature of a 3.5 carat diamond from -50°C to 250°C?

Short Answer

Expert verified

The amount of heat is 146J

Step by step solution

01

Definition of temperature

Temperature is measured by coldness and hotness which are accounted for with different scales.

02

Finding the amount of heat 

The temperature difference belongs from 223k to 523K and m=7×10-4Kg

According to the definition of the specific heat c, the temperature raise from 2.5T to 350

Then

localid="1649151436820" Qm=∫T1T2c(T)dT=∫T1T2(2.5T-350)dT=(1.4T-350T)223523Qm=2.08×105J×Kg

Now

Q=m∫T1T2c(T)dT=2.08×105J×Kg×7×10-4=146J

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Most popular questions from this chapter

FIGURE P19.62 shows a thermodynamic process followed by 120mgof helium.

a. Determine the pressure (in atm), temperature (in C∘), and volume in (cm3)of the gas at points 1,2 , and 3 . Put your results in a table for easy reading.

b. How much work is done on the gas during each of the three segments?

c. How much heat energy is transferred to or from the gas during each of the three segments?

512 g of an unknown metal at a temperature of 15°C is dropped into a 100 g aluminum container holding 325 g of water at 98°C. A short time later, the container of water and metal stabilizes at a new temperature of 78°C. Identify the metal.

2.0molof gas are at 30°Cand a pressure of 1.5atm. How much work must be done on the gas to compress it to one-third of its initial volume at (a) constant temperature and (b) constant pressure? (c) Show both processes on a singlepVdiagram.

The gas cylinder in Figure Q19.11 is well insulated on all sides. The piston can slide without friction. Many small masses on top of the piston are removed one by one until the total mass is reduced by 50%.

a. During this process, are (i) ∆T, (ii) W, and (iii) Q greater than, less than, or equal to zero? Explain.

b. Draw a pV diagram showing the process.

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