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# Change of density with temperature

Before to go with tis topic students must know the topic thermal expansion of matter, which is one of the most important topic for thermal properties of matter. To learn the topic Thermal expansion of matter CLICK HERE-

After Completing the topic thermal expansion   students must solve some important questions of thermal expansion of matter, To get (solve)the question  based on this topic CLICK HERE-

Change of density with temperature

The density of a substance is defined as its mass per unit volume of a given mass of a substance changes with temperature while its mass remain the same , the density undergoes a change with the temperature .

Consider a body of mass m . Let v1 and ƍ1 be its volume and density respectively at temperature t1 and v1and ƍ2 the corresponding values at t2.

Clearly , mass m= v2ƍ2=v1(1+ƳΔT)ƍ2, where ΔT=t2-t1 ,

Thus ƍ2 = ƍ1/(1+ƳΔT) = ƍ1(1+ƳΔT)-1. = ƍ1(1-ƳΔT)[ Using Binomial theorem]

i.e.  ƍ2= ƍ1(1-ƳΔT) [so we can say the density of the material decreases with the rise in temperature].

Some numericals  for practice based on change of density with temperature are given below .

1. Coefficient of volume expansion of mercury is 0.18 x 10-3/0C . If the density of mercury at 00C is 13.6g/cc, then its density at 2000C is (a) 13.11g/cc (b)52.11g/cc (c)16.11g/cc (d) 26.11g/cc.

2. The coefficient of volume expansion of glycerin is 49×10-5/K. The fractional change in density on a 300C rise in temperature is (a)1.47 x 10-2 (b) 1.47 x 10-3 (c) 1.47 x 10-1 (d) 1.47 x 10-4.