Expansion Of Gases
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Card # 35‐Expansion of Gases Gases don’t have definite shape therefore they have only volume expansion. Since the expansion of container is negligible in comparison to the expansion in gases, therefore gases have only real expansion. Gases can be expanded in two ways. 1. Keeping pressure constant, the volume can be changed by temperature Coefficient of volume expansion = Yα = Increase in volume of gases Original volume of gas x change in temperature Yα = ΔV V0ΔT 2. Keeping volume constant, pressure can be changed by temperature Coefficient of volume expansion Yβ = Increase in pressure Original pressure x change in temperature Yβ = ΔP P0 ΔT In case of ideal gas we know that PV = RT According to Boyle’s law PV= constant
P V
o
= P V
o
P0V0 (1 + Yα ΔT) = P0V0 (1 + Yβ ΔT) (1 + Yα ΔT) = (1 + Yβ ΔT P0V0) Yα ΔT = Yβ ΔT Therefore Yα = Yβ = 1/273˚C-1 Newton’s Law of Cooling Under the conditions of natural convection rate of cooling i.e. rate of loss of heat is directly proportional to temperature difference between the body and surrounding. Rate of loss of heat α Temperature difference between body and surrounding d Q α (θ − θ o ) d t
d Q d t
=
−
K
(θ
−
θ
o
)
Negative sign (-) shows that rate of loss decreases with time. This curve is showing cooling of hot water with time. Cooling of hot water depends on the difference of its temperature from that of the surroundings. Initially the rate of cooling is higher and decreases as the temperature of the body falls. Newton’s law of cooling is applicable when a body is cooling under conditions of natural convection and the temperature difference between the body and surrounding is small (< 30o C )
P V
o
= P V
o
P0V0 (1 + Yα ΔT) = P0V0 (1 + Yβ ΔT) (1 + Yα ΔT) = (1 + Yβ ΔT P0V0) Yα ΔT = Yβ ΔT Therefore Yα = Yβ = 1/273˚C-1 Newton’s Law of Cooling Under the conditions of natural convection rate of cooling i.e. rate of loss of heat is directly proportional to temperature difference between the body and surrounding. Rate of loss of heat α Temperature difference between body and surrounding d Q α (θ − θ o ) d t
d Q d t
=
−
K
(θ
−
θ
o
)
Negative sign (-) shows that rate of loss decreases with time. This curve is showing cooling of hot water with time. Cooling of hot water depends on the difference of its temperature from that of the surroundings. Initially the rate of cooling is higher and decreases as the temperature of the body falls. Newton’s law of cooling is applicable when a body is cooling under conditions of natural convection and the temperature difference between the body and surrounding is small (< 30o C )
