Como os líquidos não têm forma própria, quando são aquecidos, dilatam-se juntamente com o recipiente que os contêm. Tal fato dificulta a determinação da dilatação dos líquidos, porque o recipiente também aumenta de volume. Geralmente, para uma mesma variação de temperatura, a dilatação dos líquidos é maior do que a de sólidos e, por isso, se um recipiente estiver completamente cheio de um líquido, o aumento da temperatura do conjunto virá acarretar transbordamento.
Temos um recipiente cilíndrico de vidro de volume 200 cm3, contendo 180 cm3 de querosene. Inicialmente o conjunto está a uma temperatura de 20ºC.
Sabendo que o coeficiente de dilatação volumétrica do vidro e do querosene são, respectivamente, 1,0 x 10 – 5ºC1 e 1,0 x 10 – 3 ºC-1, qual é a máxima temperatura a que se pode submeter o conjunto sem que o querosene transborde?
- A) 182ºC.
- B) 132ºC.
- C) 152ºC.
- D) 82ºC.
- E) 32ºC.
Resposta:
Para resolver essa questão, we need to understand the concept of thermal expansion. When a liquid is heated, it expands, and its volume increases. However, since the container is also expanding, it's challenging to determine the exact volume expansion of the liquid. In this case, we need to consider the thermal expansion of both the querosene and the glass container.
The coefficient of volume expansion for the glass is 1.0 x 10^-5 °C^-1, and for the querosene, it's 1.0 x 10^-3 °C^-1. We can use these values to calculate the maximum temperature to which the system can be heated without the querosene overflowing.
Let's start by identifying the initial conditions: the container has a volume of 200 cm³, and it's filled with 180 cm³ of querosene at an initial temperature of 20°C. We want to find the maximum temperature (T) at which the querosene will just start to overflow.
First, we need to calculate the volume expansion of the querosene and the container. The volume expansion of the querosene can be calculated using the formula:
$$Delta V_q = V_q cdot alpha_q cdot Delta T$$where ΔV_q is the volume expansion of the querosene, V_q is the initial volume of the querosene (180 cm³), α_q is the coefficient of volume expansion of the querosene (1.0 x 10^-3 °C^-1), and ΔT is the temperature change.
Similarly, the volume expansion of the container can be calculated using:
$$Delta V_c = V_c cdot alpha_c cdot Delta T$$where ΔV_c is the volume expansion of the container, V_c is the initial volume of the container (200 cm³), α_c is the coefficient of volume expansion of the container (1.0 x 10^-5 °C^-1), and ΔT is the temperature change.
Since the querosene will overflow when the total volume expansion of the querosene and the container equals the remaining volume in the container (20 cm³), we can set up the equation:
$$Delta V_q + Delta V_c = 20$$Substituting the values, we get:
$$180 cdot 1.0 cdot 10^-3 cdot Delta T + 200 cdot 1.0 cdot 10^-5 cdot Delta T = 20$$Solving for ΔT, we get:
$$Delta T = 112°C$$Therefore, the maximum temperature to which the system can be heated without the querosene overflowing is:
$$T = 20°C + 112°C = 132°C$$So, the correct answer is B) 132°C.
This problem illustrates the importance of considering the thermal expansion of both the liquid and the container when dealing with thermal expansion problems. By using the coefficients of volume expansion and the initial conditions, we can calculate the maximum temperature to which the system can be heated without the liquid overflowing.
Deixe um comentário