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Chapter 12: Q32P (page 509)

A block100-gof metal at a temperature of20°Cis placed into an insulated container with 400g of water at a temperature of0°C. The temperature of the metal and water ends up at 2°C . What is the specific heat of this metal, per gram? Start from the Energy Principle. The specific heat of water is 4.2 J/K/g.

Short Answer

Expert verified

The specific heat of this metal is 1.86 J/K/g.

Step by step solution

01

Given data

Mass of the metal mm=100g

Initial temperature of metal tm=20°C

Mass of watermw=400g

Initial temperature of watertw=0°C

Final temperatureT=2°C

Heat capacity of water cw=4.2J/K/g

02

Definition of specific heat

Heat capacity is a physical property of matter, defined as the amount

of the heat to be supplied to an object to produce a unit change in its

temperature.

03

Determine the specific heat of metal

Heat lost by metal = Heat gain by water

mmcm20°C-2°C=mwcw20°C-2°C⇒100cm18=4004.22cm=4004.2210018=1.86J/K/g

Hence, specific heat of metal will be cm=1.86J/K/g.

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Most popular questions from this chapter

The reasoning developed for counting microstates applies to many other situations involving probability. For example, if you flip a coin 5 times, how many different sequences of 3 heads and 2 tails are possible? Answer: 10 different sequences, such as HTHHT or TTHHH. In contrast, how many different sequences of 5 heads and 0 tails are possible? Obviously only one, HHHHH, and our equation gives , using the standard definition thatis defined to equal 1.

If the coin is equally likely on a single throw to come up heads or tails, any specific sequence like HTHHT or HHHHH is equally likely. However, there is only one way to get HHHHH, while there are 10 ways to get 3 heads and 2 tails, so this is 10 times more probable than getting all heads.

Use the expression to calculate the number of ways to get 0 heads, 1 head, 2 heads, 3 heads, 4 heads, or 5 heads in a sequence of 5 coin tosses. Make a graph of the number of ways vs. the number of heads.

A block of copper at a temperature of 50°C is placed in contact with a block of aluminium at a temperature of45°C in an insulated container. As a result of a transfer of 2500 J of energy from the copper to the aluminium, the final equilibrium temperature of the two blocks is 48°C. (a) What is the approximate change in the entropy of the aluminium block? (b) What is the approximate change in the entropy of the copper block? (c) What is the approximate change in the entropy of the Universe? (d) What is the change in the energy of the Universe?

For a certain metal the stiffness of the interatomic bond and the mass of one atom are such that the spacing of the quantum oscillator energy levels is 1.5×10-23J. A nanoparticle of this metal consisting of atoms has a total thermal energy of role="math" localid="1657867970311" 18×10-23J. (a) What is the entropy of this nanoparticle? (b) The temperature of the nanoparticle is 87 K. Next we add18×10-23 J to the nanoparticle. By how much does the entropy increase?

How many different ways are there to get 5 heads in 10 throws of a true coin? How many different ways are there to get no heads in 10 throws of a true coin?

There was transfer of energy of 5000 J into a system due to a temperature difference, and the entropy increased by 10 J/K. What was the approximate temperature of the system, assuming that the temperature didn’t change very much?.
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