## Thursday, April 24, 2008

### Concept review Ch. 23 Heat and Temperature

Hot and cold bodies

A hot body has more internal energy than an otherwise identical cold body.

When a hot body and cold body are kept in contact, energy is transferred from hot body to cold body and the cold body warms up and hot body cools down.

The transfer to energy from a hot body to a cold body is nonmechanical process. This energy that is transferred from one body to the other, without any mechanical work involved, is called heat.

Zeroth law of thermodynamics

If two bodies A and B are in thermal equilibrium and A and C are also in thermal equilibrium then B and C are in also in thermal equilibrium

All bodies in thermal equilibrium are assigned equal temperature.

Heat flows from the body at higher temperature to the body at lower temperature

* To measure temperature, we can choose a substance and look for a measurable property of the substance which monotonically changes with temperature.

* Length of mercury in long capillary, resistance of a wire, pressure of gas when volume is kept constant are properties which can be used for temperature measurement.

Mercury Thermometer

A change in one degree of temperature results in a change of (l2–l1)/(t2-t1) in the length of mercury column. Hence the length of the capillary can be graduated in degrees.

Centigrade system assumes ice point at 0°C and the steam point at 100°C.

Another popular system known as Fahrenheit system assumes 32°F for the ice point and 212°F for the steam point

Hence conversion formula is F = 32 + 9C/5

Platinum resistance thermometer

Electric resistance of a metal wire increases monotonically with temperature and may be used to define a temperature scale. A platinum wire is often used to construct a thermometer based on this scale. Thermometer using platinum wire is called platinum resistance thermometer.

This thermometer also uses the principle of Wheatstone bridge.

Constant volume gas thermometer

The temperature of triple point of water is assigned a value of 273.16 K

The temperature of ice point on the ideal gas scale is 273.15 K and of the steam point is T = 373.15 K. The interval between the two is 100 K.

Centigrade scale or Celsius scale is defined to have ice point at 0°C and steam point at 100°C. The interval is 100°C.

Hence if θ represents the Celsius or centigrade temperature

V = T – 273.15 K

Ideal gas equation

pV = nRT

n = the amount of gas in moles
R = universal constant = 8.314 J/mol-K

Callendar’s Compensated Constant Pressure Thermometer is also there.

An adiabatic wall does not allow heat flow even between two bodies at different temperatures.

Diathermic wall allows heat transfer between two bodies at different temperatures through it rapidly.

Thermal expansion

Average coefficient of linear expansion

Average (α) = (1/L)*∆L/∆T

Coefficient of linear expansion at temperature T
α = Lim (∆T->0)(1/L)*∆L/∆T = (1/L)dL/dT

Suppose the length of a rod is L0 at 0° C and Lθ at temperature θ measured in Celsius. If α is small and constant over the given temperature interval,

α = Lθ-L0/L0*θ or

Lθ = L0(1+αθ)

The coefficient of volume expansion is defined in a similar way.

γ = (1/V)dV/dT

It is also known as coefficient of cubical expansion.

Vθ = V0(1+γθ)

γ = 3α