(b) use the first law of thermodynamic to calculate au for the following situations: (i) a coiled spring unwinds producing 153 j of work and losing 37 j as heat to friction (1 mark) (ii) an insulated bucket of water is stirred by a paddle, which provides 289 j of work. (1 mark) (iii) adding 1 kj of heat to a sample of gas in an isovolumetric process. (1 mark) (iv) the isothermal compression of a gas from 26 l to 5 l. (1 mark) (v) the isobaric expansion of a gas from 5 l to 18 l at a constant pressure of 950 kpa caused by the addition of 15.6 kj of heat.

(i) ΔU = 116 J

(ii) ΔU = 289 J

(iii) ΔU = 1 KJ

(iv) ΔU = 0 J

(v) ΔU = 3.25 KJ

Explanation:

first law:

(i) W = 153 J;  Q = - 37 J ( Q ( - ), losing friction )

⇒ ΔU = 153 - 37 = 116 J

(ii) W = 289 J; Q = 0 ( insulated)

⇒ ΔU = W = 289 J

(iii) Q = 1 KJ , W = 0 ( isovolumetric process)

⇒ ΔU = Q = 1 KJ

(iv) isothermal ( constant temperature )

∴ ΔT = 0° ( isothermal )

⇒ ΔU = 0 J

(v) isobaric ( constant pressure )

⇒ ΔU = Q + W

∴ Q = 15.6 KJ

∴ W = - ∫ P dV = - P ΔV;  W (-) the system performs a job and the volume increases

.

∴ P = 950 KPa * ( 1000 Pa / KPa ) = 950000 Pa = 950000 J/m³

∴ ΔV = 18 - 5 = 13 L * ( m³ / 1000 L ) = 0.013 m³

⇒ W = - ( 950000 J/m³) * ( 0.013 m³ ) = - 12350 J ( - 12.35 KJ )

⇒ ΔU = 15.6 KJ + ( - 12.35 KJ )

⇒ ΔU = 3.25 KJ