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Chapter 19: Q. 18 (page 543)

A scientist whose scale is broken but who has a working

2.5 kW heating coil and a thermometer decides to improvise

to determine the mass of a block of aluminum she has recently

acquired. She heats the aluminum for 30 s and finds that its

temperature increases from 20C to 35C. What is the mass of the

aluminum?

Short Answer

Expert verified

The mass of the aluminum ism=5.643[kg]

Step by step solution

01

Given information

The coil's power is2.5kW, it runs for 30seconds, and the temperature increment is150cIt's an aluminium block.

02

Calculation

formula used:

The heat provided by the heating coil is:

Q=PΔt

From aluminum property table:

Cp=0.886JgΔ°C

The heating coil was turned on 30 seconds, and the heat produced is:

Q=2.5[kW]Δ30[s]=75[kJ]=75,000[J]Q=mΔ0.886JgΔ°CΔ35C∘-20C∘=75,000[J]

Solving for m:

m=75,000[J]0.886J8Δ°CΔ35C∘-20C∘=5,643[g]m=5.643[kg]

We could compute the block's mass by supposing it absorbed all of the heat. This isn't always the case, and the mass will be smaller.

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Most popular questions from this chapter

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?

A typical nuclear reactor generates 1000 MW (1000 MJ/s) of electrical energy. In doing so, it produces 2000 MW of “waste heat” that must be removed from the reactor to keep it from melting down. Many reactors are sited next to large bodies of water so that they can use the water for cooling. Consider a reactor where the intake water is at 18°C. State regulations limit the temperature of the output water to 30°C so as not to harm aquatic organisms. How many liters of cooling water have to be pumped through the reactor each minute?

Two cylinders each contain 0.10molof a diatomic gas at 300Kand a pressure of 3.0atm. Cylinder A expands isothermally and cylinder B expands adiabatically until the pressure of each is 1.0atm.

a. What are the final temperature and volume of each?

b. Show both processes on a single pVdiagram. Use an appropriate scale on both axes.

A cylinder with a movable piston contains nmoles of gas at a temperature higher than that of the surrounding environment. An external force on the piston keeps the pressure constant while the gas cools as ΔT=(ΔT)0e-t/τ, where ΔTis the temperature difference between the gas and the environment, (ΔT)0is the initial temperature difference, andτ is the time constant.

a. Find an expression for the rate at which the environment does work on the gas. Recall that the rate of doing work is power.

b. What power is initially supplied by the environment if 0.15molof gas are initially 12°Cwarmer than the surroundings and cool with a time constant of 60s?

How much work is done on the gas in the process shown in Figure EX19.1?
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