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Determine the Kelvin temperature for each of the following:

(a) human body temperature;

(b) the boiling point of water(at the standard pressure of 1 atm);

(c) the coldest day u can remember;

(d) the boiling point of liquid nitrogen(-196°C);

(e) the melting point of lead(327°C)

Short Answer

Expert verified

(a)310.15K(b)373.15K(c)277.15K(d)77.15K(e)600.15K

Step by step solution

01

Part (a): Step 1. Given information

The human body temperature in Celsius scale is 37°C.

02

Part (a) Step 2: Calculation

The relation between the temperature in Kelvin scale and that in Celsius scale is given by

K=C+273.15...................(1)

Here, Kis the temperature in Kelvin scale and Cis that in Celsius scale.

Substitute 37for Cinto equation (1) to calculate the required value.

K=37+273.15=310.15K

03

Part (b) Step 1: Given information

The boiling point of water at standard pressure is 100°C.

04

Part (b): Step 2. Calculation

Substitute 100for Cinto equation (1) to calculate the required value.

K=100+273.15=373.15K

05

Part (c): Step 1. Given information

The coldest day that can be remembered is 4°C.

06

Part (c): Step 2. Calculation

Substitute 4for Cinto equation (1) to calculate the required value.

K=4+273.15=277.15K

07

Part (d): Step 1. Given information

The boiling point of liquid nitrogen is -196°C.

08

Part (d): Step 2. Calculation

Substitute -196for Cinto equation (1) to calculate the required value.

K=-196+273.15=77.15K

09

Part (e) : Step 1. Given information

The melting point of lead is 327°C.

10

Part (e): Step 2. Calculation

Substitute 327for Cinto equation (1) to calculate the required value.

K=327+273.15=600.15K

11

Final answer

The required temperatures are as follows:

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Most popular questions from this chapter

Calculate the heat capacity of liquid water per molecule, in terms of K . Suppose (incorrectly) that all the thermal energy of water is stored in quadratic degrees of freedom. How many degrees of freedom would each molecule have to have?

When the temperature of liquid mercury increases by one degree Celsius (or one kelvin), its volume increases by one part in 550,000 . The fractional increase in volume per unit change in temperature (when the pressure is held fixed) is called the thermal expansion coefficient, β :
β≡ΔV/VΔT
(where V is volume, T is temperature, and Δ signifies a change, which in this case should really be infinitesimal if β is to be well defined). So for mercury, β =1 / 550,000 K-1=1.81 x 10-4 K-1. (The exact value varies with temperature, but between 0oC and 200oC the variation is less than 1 %.)
(a) Get a mercury thermometer, estimate the size of the bulb at the bottom, and then estimate what the inside diameter of the tube has to be in order for the thermometer to work as required. Assume that the thermal expansion of the glass is negligible.
(b) The thermal expansion coefficient of water varies significantly with temperature: It is 7.5 x 10 -4 K-1 at 100oC, but decreases as the temperature is lowered until it becomes zero at 4oC. Below 4oC it is slightly negative, reaching a value of -0.68 x 10-4K-1 at 0oC. (This behavior is related to the fact that ice is less dense than water.) With this behavior in mind, imagine the process of a lake freezing over, and discuss in some detail how this process would be different if the thermal expansion coefficient of water were always positive.


Put a few spoonfuls of water into a bottle with a tight lid. Make sure everything is at room temperature, measuring the temperature of the water with a thermometer to make sure. Now close the bottle and shake it as hard as you can for several minutes. When you're exhausted and ready to drop, shake it for several minutes more. Then measure the temperature again. Make a rough calculation of the expected temperature change, and compare.


Make a rough estimate of the thermal conductivity of helium at room temperature. Discuss your result, explaining why it differs from the value for air.

Heat capacities are normally positive, but there is an important class of exceptions: systems of particles held together by gravity, such as stars and star clusters.
aConsider a system of just two particles, with identical masses, orbiting in circles about their center of mass. Show that the gravitational potential energy of this system is-2times the total kinetic energy.
bThe conclusion of part aturns out to be true, at least on average, for any system of particles held together by mutual gravitational attraction:

U¯potential=−2U¯kinetic

Here each Urefers to the total energy (of that type) for the entire system, averaged over some sufficiently long time period. This result is known as the virial theorem. (For a proof, see Carroll and Ostlie (1996), Section 2.4.) Suppose, then, that you add some energy to such a system and then wait for the system to equilibrate. Does the average total kinetic energy increase or decrease? Explain.

cA star can be modeled as a gas of particles that interact with each other only gravitationally. According to the equipartition theorem, the average kinetic energy of the particles in such a star should be 32KT, whereT is the average temperature. Express the total energy of a star in terms of its average temperature, and calculate the heat capacity. Note the sign.
dUse dimensional analysis to argue that a star of mass Mand radius Rshould have a total potential energy of -GM2/R, times some constant of order 1.
eEstimate the average temperature of the sun, whose mass is 2×1030kgand whose radius is 7×108m. Assume, for simplicity, that the sun is made entirely of protons and electrons.

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