Show that if the room temperature changes by a small amount from `T to T +/_\T`, the fundamental frequency of an organ pipe changes from `v to v + /_\v, where
`(/_\v)/v=1/2(/_\T)/T`.

The room temperature charges by a small amount from T to T+DeltaT (on Kelvin scale). The fundamental frequency of organ pipe changes from f to f+Deltaf , then

The room temperature charges by a small amount from T to T+DeltaT (on Kelvin scale). The fundamental frequency of organ pipe changes from f to f+Deltaf , then

The room temperature charges by a small amount from T to T+DeltaT (on Kelvin scale). The fundamental frequency of organ pipe changes from f to f+Deltaf , then

The pressure p, volume V and temperature T for a certain gas are related by p = (AT - BT^(2))/V , where A and B are constants. The work done by the gas when the temperature changes from T_(1) to T_(2) while the pressure remains constant, is given by

An ideal gas has molar heat capecity C_(v) at constant volume. The gas undergoes a process where in the temperature changes as T=T_(0)(1+alphaV^(2)) , T and V are temperature and volume respectively, T_(0) and alpha are positive constant.The molar heat capecity C of the gas is given as C=C_(v)+Rf(V), where, f (V) is a funtion of volume. The expression for f (V) is

Pressure P, volume V and temperature T for a certain gas are related by P=(AT-BT^(2))/(V) , where A and B are constatns .The work done by the gas as its temperature change from T_(1) to T_(2) while pressure remaining constatn is