A brass rod and a steel rod are both measured at $0^{o} C$ and their lengths found to be 120 cm and 120.2 cm respectively. At what temperature are their lengths equal?
$(α_{b r a s s} = 12 \times 10^{- 6}^{o} C^{- 1}, α_{s t e e l} = 17 \times 10^{- 6}^{o} C^{- 1})$

Open in App

Solution

Let temperature at which the lengths of brass rod $(l_{b})$ and a steel rod $(l_{s})$ are equal
$l_{b} = l_{s}$
$l_{0} (1 + α b Δ θ) = l_{0}^{1} (1 + α_{s} Δ θ)$
$120 (1 + 12 \times 10^{- 6} \times θ) = 120.2 (1 + 17 \times 10^{- 6} \times θ)$
$120 + 120 \times 12 \times 10^{- 6} \times θ = 120.2 + 120.2 \times 17 \times 10^{- 6} θ$
solving we get,
$θ = {57.415}^{o} C$

Suggest Corrections

Similar questions

Q. A brass rod and a steel rod are both measured at

0^{\circ}

C. Their lengths are found to be 150 cm and 150.2 cm respectively. At what common temperature will their lengths be equal?
(

α_{s t e e l} = 12 \times 10^{- 6} /^{\circ}

α_{b r a s s} = 18 \times 10^{- 6} /^{\circ}

Q. The length of a steel rod is

5 c m

greater than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be:

[Coefficient of linear expansion for steel and brass are

12 \times 10^{- 6} /^{\circ} C

and

18 \times 10^{- 6} /^{\circ} C

respectively]

Q. A copper rod and a steel rod maintain a difference in their lengths constant= 10 cm at all temperatures. If their coefficients of expansion are

1.6 \times 10^{- 5} K^{- 1}

and

1.2 \times 10^{- 5} K^{- 1}

, then the length of the Cu rod is

At $40^{\circ} C$ , a brass rod has a length 50 cm and a diameter 3.0 mm. It is joined to a steel rod of the same length and diameter at the same temperature. What is the change in the length of the composite rod when it is heated to $240^{\circ} C$ ? The coefficients of linear expansion of brass and steel are $2.0 \times 10^{- 5}^{\circ} C^{- 1}$ and $1.2 \times 10^{- 5}^{\circ} C^{- 1}$ respectively.

Q. A steel rod is 3.000 cm in diameter at

25^{\circ} C

. A brass ring has an interior diameter of 2.992 cm at

25^{\circ} C

. At what common temperature will the ring just slide on to the rod.

α_{s t e e l} = 12 \times 10^{- 6} K^{- 1}

and

α_{b r a s s} = 18 \times 10^{- 6} K^{- 1}

Join BYJU'S Learning Program

A brass rod and a steel rod are both measured at 0oC and their lengths found to be 120 cm and 120.2 cm respectively. At what temperature are their lengths equal?(αbrass=12×10−6oC−1,αsteel=17×10−6oC−1)

Let temperature at which the lengths of brass rod (lb) and a steel rod (ls) are equallb=lsl0(1+αbΔθ)=l10(1+αsΔθ)120(1+12×10−6×θ)=120.2(1+17×10−6×θ)120+120×12×10−6×θ=120.2+120.2×17×10−6θsolving we get,θ=57.415oC

A brass rod and a steel rod are both measured at $0^{o} C$ and their lengths found to be 120 cm and 120.2 cm respectively. At what temperature are their lengths equal?
$(α_{b r a s s} = 12 \times 10^{- 6}^{o} C^{- 1}, α_{s t e e l} = 17 \times 10^{- 6}^{o} C^{- 1})$