Question

A copper cube of side of length 1 cm is subjected to a pressure of 100 atmosphere. Find the change in its volume, if the bulk modulus of copper is 1.4 × 10¹¹ N m⁻². (1 atmosphere = 1 × 10⁵ N m⁻²).

Answer 1

side length of copper cube , L = 1cm = 10^-2 m
volume of copper cube , V = L³ = 10^-6 m³
pressure subjected to copper cube , P = 100atm
we know, 1 atm = 10^5 N/m²
so, pressure subjected to copper cube , P = 10^7 N/m²
bulk modulus of copper , B = 1.4 × 10¹¹ N/m²

now, Bulk modulus, B = Pressure/volume strain
we know, volume strain = ∆V/V

so, B = P/(∆V/V)

1.4 × 10¹¹ N/m² ={ 10^7N/m²}/{∆V/10^-6 m³}

1.4 × 10¹¹ = 10¹³/∆V

∆V = 1.4/100 = 0.014 m³

hence, change in volume of copper cube is 0.014m³

Answer 2

Explanation:

A copper cube of side of length 1 cm is subjected to a pressure of 100 atmosphere. Find the change in its volume, if the bulk modulus of copper is 1.4 × 10¹¹ N m⁻². (1 atmosphere = 1 × 10⁵ N m⁻²).