The coefficient of cubical expansion of mercury is $$0.00018/$$°C and that of brass $$0.00006$$ $$/$$°C. If a barometer having a brass scale were to read $$74.5$$ cm at $$30$$°C, find the true barometric height at $$0$$°C. The scale is supposed to be correct at $$15$$°C.

Question

Infinity Learn · Accepted Answer

As,  αbrass $$=$$γbrass $$3=0.000063$$                   $$=0.00002=2$$×$$10-5/C$$  ∘The brass scale is true at $$15$$°C, therefore at $$30$$°, its graduations will increase in length and hence, observed reading will be less than actual reading at $$30$$°.∴The change in reading.                    Δ$$l=l$$αbrass $$($$Δ$$T)=74.5$$×$$2$$×$$10-5(30-15)$$                        $$=$$ $$0.02235$$ cm∴ Actual reading at $$30$$°C,                      $$l30=lobserved$$ $$+$$Δ$$l=74.5+0.02235=74.522$$ cmAssuming area of $$cross-section$$ to be constant, we have                     $$V0$$ρ$$0$$ $$=$$ $$V30$$ρ$$30or$$                $$ah0$$ρ$$0$$ $$=$$ $$ah30$$ρ$$30Therefore$$, true height at $$0$$°C,                 $$h0=h30$$ρ$$30$$ρ$$0=h301+$$γHgΔT                      $$=74.5221+0.00018$$×$$30=74.5221.0054=74.122$$ cm

The coefficient of cubical expansion of mercury is 0.00018/°C and that of brass 0.00006 /°C. If a barometer having a brass scale were to read 74.5 cm at 30°C, find the true barometric height at 0°C. The scale is supposed to be correct at 15°C.

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!